
Gass. 



Book Mft 



I&&7 



[BY 

F ENqiME£R3,U.5.ARMy, 



THE 



PLANETARY 



AND 



STELLAR WORLDS 

A POPULAR EXPOSITION OF THE GREAT DISCOVERIES AND 
THEORIES OF MODERN ASTRONOMY. 



BY 



Gen. O. M. MITCHEL. 



NEW YORK: 

John B. Alden, Publisher. 

1887. 






I Transfer 



Engineers School Lib*. 
June 29, 931 



TABLE OF CONTENTS. 






LECTUEE I. 



An Exposition of the Problem which the Heavens Present for Solution. 



First revolution of the Heavens witnessed by man, 11 

The curiosity excited and its effects, 12 

Object of the course, 12 

Th« astronomer lives in all ages, 13 

First problem to distinguish between real and 

apparent motion, 14 

The relations of the sun, and earth, and moon, ... 15 

The wandering stars or planets, 15 

Fixed stars, points of reference, 16 

Complexity of the planetary movement*, If 

Discovery of the true centre of motion, 17 



The planets form a system; their orbits, laws, 

stability, 18 

Perturbations, 19 

Analytic machinery, 19 

Examination of the starry heavens 20 

Distance of the fixed stars to be determined, 20 

Motions among the stars, 21 

Binary systems, movement of the sun in space,.. .. 21 
Investigations yet to be made, and probable 
success, 22 



LECTUEE II. 



The Discovery of the Primitive 

The founder of the science of astronomy unknown, 

First discovery on the moon, 

Her motion among the stars and her phases, 

Cause of the phases sought; two revolutions of 
the moon discovered, 

First ideas of the constellations ; North Star, . ... 

Motions of the sun and moon among the stars; 
the starry heavens surround the earth, 

First measure of the year, 

A moving star discovered, 

Periods of the planets determined, 

The sun's apparent motion the subject of per- 
plexity, 



Ages. 



The equinoxes and solstices, — 83 

Inequality in the sun's motion detected, 34 

The construction of the sphere, 34 

Its uses in observing, 34 

Eclipses of the sun and moon, and their effects, ... 35 
Explanation of solar eclipses; discovery of the 
moon's reflective light, and explanation of her 

phases, 35 

Lunar eclipses explained, 36 

Prediction of the first eclipse, §8 

Value of recorded eclipses, 39 



LECTUEE III. 

Theories for the Explanation of the Motions of the Heavenly Bodies. 



The names of early discoverers lost, 41 

Chaldean period found among many nations, 41 

The days of tbe week, and their names; place of 

the vernal equinox, 42 

Precession of the equinoxes, 43 

Astronomy of the primitive ages, and condition of 
the mind at the beginning of the era reached 

by history, 44 

Causes retarding the progress of astronomy, 45 

The confounding of true and apparent motion ; im- 
mobility of the earth and its central position, 45 
The Greek astronomers, Pythagoras, Nicetas, 
Hipparchus, Ptelemy, 46 



System of Ptolemy 48 

Astronomy cultivated by the Arabs, 48 

The era of modern science commences, 43 

Copernicus and his discoveries, 49 

His system promulged with great caution, 51 

Kepler, the character of his mind, his mode of 

research, 52 

His great discoveries; he finds the orbits of the 

planets, 53 

Detects his second law, 54 

His efforts to find the third law successful, 57 

Important ©f those laws, • 57 



TABLE OF CONTENTS. 



LECTUKE IV. 

Discovery of the Great Laws of Motion and Gravitation. 



The philosophy of Aristotle— its hold on the mind, 59 

Characteristics of Galileo's mind, 59 

He detects the errors of Aristotle, 60 

Attacks his theories, and demonstrates their false- 
hood by experiment, 60 

Driven from Pisa by his enemies, 61 

Discovers the law of falling bodies, 61 

Adopts the Copernican theory, 62 

Constructs a telescope, 62 

His discoveries in the moon, and among the plan- 
ets and fixed stars, 63 

Phases of Venus, 64 

Questions relating to the planetary motions, 65 

Laws of motion; the centrifugal force, 66 



Problem presented for solution to Newton, 6? 

Conjectures of Kepler ; discoveries of Descartes, . . 67 
Measure of the moon's distance and of the earth's 

circumf erence 68 

The law of gravitation — Newton's first effort to 

demonstrate the truth of this law, 69 

He finally shows that the moon is ever falling 

towards the earth, and proves the law, 71 

Enunciation of his great law, 72 

Discovers that the planets may revolve in conic 

sections, 73 

Contrast between Kepler's and Newton's methods 

of research, 73 



LECTUKE V. 



Universal Gravitation Applied to the Explanation of the Phenomena of 
the Solar System. 

Perplexity occasioned by the seeming discrepancy 
between the observed and computed motion of 



The era of physical astronomy commences, 75 

A theoretic system proposed and discussed, a 
central sun and solitary planet, . . 76 

Planets and satellites added and their effects con- 
sidered, 77 

How the imagined system may be made the sys- 
tem of nature, 78 

Discussion of the relative motions of the sun, 
moon, and earth, under the action of their 
mutual influences, 78 

Tke moon's acceleration ; motion of her apsides, 
nodes, etc., and the discovery of the change 
in the figure of the earth's orbit, 81 



the moon's perigee 84 

Finally removed by Clairault, 85 

Changes in the earth's figure occasioned by its 

rotation, 86 

The form of equilibrium reached, 88 

The precession of the equinoxes caused by the 

protuberant matter at the earth's equator, 89 

Moon affected by the redundant matter at the 

earth's equator, 91 

Wonderful questions answered by an examination 

of the moon, 81 



LECTUKE VI. 



The Stability of the Planetary System. 



Rapid survey of the system, 93 

General characteristics of the planets, 94 

What phenomena gravitation must account for, . . 95 

Stability not the sole object of the Creator, 95 

Laws of matter selected in wisdom, 96 

By how much does the central force diminish the 

primitive velocity of the planet? 97 

Changes in the elements of the orbits of the 

planets, 98 

The eccentricity, 100 



Stability of the principal axes, 100 

Motion of the perihelion, 100 

The inclinations, 102 

The lines of nodes, 103 

The periodic times, 103 

Stability of the great system, 104 

Of the system of the earth and moon, 105 

Of Jupiter's system, 106 

Of Saturn's system, 106 



LECTUKE VII. 



The Discovery of the New Planets. 

Kepler's speculations, 109 

Discovery of Uranus, 110 

Bode's law of interplanetary spaces, 110 

The astronomical congress of Lilienthal, in 1800,. .111 
Plazzi's discovery of a new planet, Ceres; its loss 
and rediscovery, 112 



The symmetry of the system destroyed by the dis- 
covery of Pallas, 114 

01bers*s theory of the bursting of a planet, 114 

Discovery of Juno and Vesta, 114 

Hencke discovers Astrea and Hebe, 115 

Hind discovers Iris and Flora, 116 



TABLE OF CONTENTS. 



Lecture TIL, The Discovery of the New Planets. — Qonbmued. 

The hypothetical planet found by Galle, of Berlin, 121 

A.dams"s computations, 122 

The new planet detected by its disc, 122 

Walker's computations, 128 

Pierce's views, 124 

Leverrier claims Neptune to be the planet of 
theory, 124 



Search for a planet beyond Uranus commenced, . . llf> 

Causes of this sear oh, 116 

Leverrier's researches on Mercury, 117 

Its transit in May, 1845, 118 

Leverrier presents his computations to the French 

Academy, 119 

Popular exhibition of his reasoning, 119 



The Cometarj Worlds. 



LECTUKE Yin. 



Characteristics of comets, 125 

Reduced to law by Newton, 126 

The comet of 1680, 126 

Halley's comet of 1682, 126 

Its return in 1759 predicted, 128 

Its return in 1835, 129 

Wonderful changes in its magnitude, 180 

Encke's comet, 131 

Approaching the sun, 131 

Resisting medium, 133 

Biela's comet, 133 

Fears excited of collision with the earth in 1832... . 134 



Its nebulous character, — ,_ 134 

Its double character in 1846. Separation of the 

comets, 135 

Vast periods of some comets, 136 

Comets seem to transit the sun's disc, 137 

Comets accounted for by Laplace's nebular hypo- 
thesis 138 

Herschel's theory of the physical condition of 

comets, 139 

His theory accounts for the diminishing period of 

Encke's comets, 140 

Zodiacal light, 140 



LECTUKE IX. 

The Scale on Which the Universe is Built. 

Scale of the planetary system, 143 , Bradley's researches for parallax, 148 

Radius of the earth's orbit too small a unit, 143 Discovery of nutation and its value, 149 

The velocity of light determined from the eclipses ' Discovery of aberration— its explanation, 150 

of Jupiter's satellites, and employed as a unit, 144 Herschel's researches for parallax, 151 

Parallax of the fixed stars, 145 Discovery of the revolving stars, 152 

No parallax sensible to the naked eye, 146 ' Power of modern telescopes, .... 153 

Great distance of the fixed stars inferred from I Bessel discovers the parallax of 61 Cygni, 164 

this fact, 146 



LECTUKE X. 

The Motions and Revolutions of the Eixed Stars. 



Distances separating man from the stars 163 

Various difficulties in the research for their 

motions, . . 163 

Hipparchus discovers a new and brilliant star, 164 

The new star of 1572, 165 

The new star of 1604, 165 

The disappearance of old stars, 166 

Changes of Algol, . . , 166 

Periodical stars, 166 

Gravitation extended to the sphere of the fixed 

stars, 167 

Periods of some of the binary systems, 168 

Herschel sounds the depth of the Milky Way, 169 



Seeks the direction of the solar motion, 189 

His reasoning, 170 

Argelander's research for the point towards which 

the solar system is moving, 172 

Struve's investigation for the quantity of angular 

motion of the system, as seen from stars of the 

first magnitude, 173 

His father's research for the relative distances of 

stars of different magnitudes, 174 

Peters's research for the parallax of stars of the 

second magnitude 175 

Maedler's theory of the central sun, 179 

| The attributes of God as displayed in the universe, 182 



PREFACE. 



A few words In explanation of the circumstances under which this volume is presented 
to the public may not be unacceptable to the reader. It is now a little more than six years 
since the writer conceived the idea of erecting a great astronomical observatory in the city of 
Cincinnati. My attention had been for many years directed to this subject, by the duties of 
the professorship, which I then held in the college. In attempting to communicate the great 
truths of astronomy, there were no instruments at hand, to confirm and fix the wonderful 
facts recorded in the books. Up to that period our country, and the West particularly had 
given but little attention to practical astronomy. A few individuals, with a zeal and ardor 
deserving of all praise, had struggled on to eminence almost without means or instruments. 
An isolated telescope was found here and there scattered through the country ; but no regu- 
larly organized observatory with powerful instruments existed within the limits of the 
United States, so far as I know. 

To attempt the building of an observatory of the first class, and to furnish it with instru- 
ments of the highest order, without any aid from the general or state government, but by the 
voluntary contribution of all classes of citizens, was an enterprise of no common difficulty. 
To ascertain whether any interest could be excited in the public mind in favor of astronomy, 
in the spring of 1842 a series of lectures was delivered in the hall of the Cincinnati College. 
To give an increased effect to these discourses (which were unwritten, and in a style of great 
simplicity), a mechanical contrivance was prepared, by the aid of which the beautiful tele- 
scopic views in the heavens were presented to the audience, with a brilliancy and power 
scarcely inferior to that displayed by the most powerful telescopes. To this fortunate in- 
vention were these lectures, no doubt, principally indebted for the interest which they pro- 
duced and which occasioned them to be attended by a very large number of the intelligent 
persons in the city. Encouraged by the large audiences, which continued through two 
months to fill the lecture-room, and still more by the request to repeat the last lecture of the 
course in one of the great churches of the city, I matured a plan for the building of an obser- 
vatory, which it was resolved should be presented to the audience at the close of the lecture 
in case circumstances should favor. Through the kindness of a few friends who were now be- 
ginning to take a deep interest in the matter, more than two thousand persons were in at- 
tendance ; and it seemed that the moment had arrived for taking the first step in an enterprise 
whose fate it was impossible to predict. 

Having closed the subject under discussion, the audience were requested to give me a few 
minutes of time, for the explanation of a matter which it was hoped would not be received 
irithout some feelings of interest and approbation. The rapid advances of astronomy in 
Europe were then referred to — the rection of observatories in all parts of the world — the 
Variety of magnificent instruments in Kussia and Germany, in France and England, and the 
utter deficiency of our own country in everything pretaining to the science of the stars. The 
past neglect was easily accounted for, and might be excused ; the future scientific character 
of the country rested with the people, and upon them devolved the responsibility of provid- 
ing the means for original research. In Europe, imperial treasure and princely munificence 
could build the temples of science ; under a free government no such means existed, and to 
accomplish the erection of these great scientific institutions, the intelligent liberality of the 
whole community was the only resource. But it had been denied that this resource could be 
relied on ; and it had been roundly asserted that, in the nature of things, the United States 
must ever remain grossly defective in all the appliances for scientific research. To test the 
truth or falsehood of these statements was not a difficult matter; and thus encouraged by the 
interest already manifested in behalf of astronomy, I had already resolved to devote jive years 
of faithful effort to accomplish the erection of a great astronomical observatory in the city 
of Cincinnati. 



§ PREFACE. 

This announcement was received with every mark of favor, and the following simple plan 
was at one presented. The entire amount required to erect the buildings and purchase the 
instruments, should be divided into shares of twenty-five dollars; every shareholder to be 
entitled to the privileges of the observatory, under the management of a board of control, to 
be elected by the shareholders. Before any subscription should become binding, the names 
of three hundred subscribers should be first obtained. This accomplished, these three hun- 
dred should meet, organize, and elect a board, who should thenceforward manage the affairs 
of the association. 

Such is the history of the Cincinnati Astronomical Society. Two resolutions were taken 
in the outset, to which I am indebted for any success which may have attended my own per- 
sonal e$orts. First : To work faithfully for five years, during all the leisure which could be 
spared from my regular duties. Second : Never to become angry, under any provocation, 
while in the prosecution of this enterprise. 

In three weeks the three hundred subscribers had been obtained. No public meeting had 
Deen called; and these names had been procured by private solicitation, and a personal expla- 
nation of the nature and advantages of the enterprise. So soon as the number was complete, 
the subscribers convened, organized, elected officers and a directory, and gave me a commis- 
sion to visit Europe, to procure instruments, examine observatories, and obtain the requisite 
knowledge to erect and conduct the institution which it was now hoped would be one day 
reared. 

This order being received, on the second day I started for New York, and on the 16th of 
June, 1842, sailed for Liverpool. Having visited many of the best appointed observatories 
both in England and on the Continent (in each and every one of which I was received with 
a degree of kindness and attention for which I acknowledge the deepest obligations), and 
having been unsuccessful in finding, either in London or Paris, an object-glass of the size 
required, I finally determined to visit the city of Munich. The fame of the optical institute 
of the celebrated Frauenhof er had even reached the banks of the Ohio ; and it was hoped 
that, in that great manufactory, an instrument such as the society desired might be obtained, 
if not completed, at least in such a state of forwardness as to permit it to be furnished at an 
early day. In this I was not disappointed. An object-glass of nearly twelve inches diame- 
ter, and of superior finish, was found in the cabinet of Mr. Mertz, the successor of Frauen- 
hofer. This glass had been subjected to a severe trial in the tube of the great refractor of 
the Munich observatory, by Dr. Lamont, and had been pronounced of the highest quality. 

To mount this glass would require about two years, at a cost of nearly ten thousand dol- 
lars ; a sum considerably greater than that appropriated at the time for an equatorial tele- 
scope. Having made a conditional arrangement for this and other instruments, I returned 
to Greenwich, England, where, at the invitation of Professor Airy, the Astronomer Royal, 
I remained for some time to study. Having accomplished the objects of my journey, I re- 
turned home, and rendered a report to a very large meeting of the members of the association 
and other citizens o£ Cincinnati. 

During my absence of four months, a great change had occurred in the commercial affairs 
of the country. Everything was depressed to the lowest point, and increased in a high ratio 
the necessary difficulties of such an undertaking, always great, even if carried forward at a 
time when the country is prosperous. 

With great difficulty the subscription was increased to an amount sufficient to warrant 
the ordering of the great object-glass already referred to. The sum of three thousand dol- 
lars was collected and remitted to meet the first payment. Even this fraction of the entire 
sum was collected with difficulty; but as the remaining part of the price of the telescope was 
not to be paid until the completion of the instrument, it was hoped that the ample time thus 
allowed would render the task of collection comparatively easy. 

The principal instrument having been ordered, and the first payment of its cost made, at- 
tention was now given to the procuring of a suitable site for the building. Fortunately for the 
society, the place of all others most perfectly adapted to their wants was then the property 
of Nicholas Longworth, Esq It is a lofty hill-top, rising some four hundred feet above the 
level of the city, and commanding a perfect horizon in all directions. On making known to 
Mr. Longworth the prospects and wants of the Astronomical Society, the writer was directed 
by him to select four acres on the hill-top, out of a tract of some twenty-five acres, and to 
proceed at once to enclose it, as it would give him great pleasure to present it to the associa- 
tion. On compliance with the conditions of the title-bond, a deed has since been received, 
placing the society in full possession of this elegant position. 



PBEFACR 9 

Preparations were now made to commence the erection of the building for the observa- 
tory. The grounds were inclosed, a road built, rendering the access to the hill-top compar- 
atively easy, the excavation for the foundations were made, and, on the 9th day of Novem- 
ber, 1843, the corner-stone of the pier which was to sustain the great Refracting Telescope, 
was laid by John Quincy Adams, with appropriate ceremonies. On this occasion Mr. Adams 
made his last great oration. The deep interest which he had taken in astronomical science 
warranted the hope that he might be induced to visit the West, on the occasion of laying 
the foundation-stone of the first great popular observatory ever erected in the United States. 
This hope was not disappointed. The unaffected devotion of this truly great man to the in- 
terests of his country were, perhaps, never more perfectly exhibited than in his ready acqui- 
escence to comply with the wishes of the astronomical society, that he should perform for 
them the important services on w r hich the future success of this new enterprise in no small 
degree depended. His high character, his advanced age, the length of the journey, the in- 
clemency of the season, all combined to exhibit to his countrymen the depth of his interest 
in a cause which could induce such sacrifices. 

After the laying of the corner-stone, the lateness of the season and other causes induced a 
suspension of the work on the building for the winter; and it was not resumed until May, 
1844. In the mean time, after incredible difficulty, the entire amount called for in the pay- 
ment for the great telescope was collected and remitted; and the society was left with 
scarcely a dollar of available means to commence the erection of a building which, accord- 
ing to the plan, would cost some seven or eight thousand dollars. 

It was believed that the intelligent mechanics of Cincinnati would lend their powerful 
aid in the accomplishment of ar enterprise which had progressed far enough to give some 
confidence in its ultimate success. With little or no means the building was commenced, 
trusting to activity and perseverance to supply the means as the work progressed. During 
the first week but three workmen were employed; but by the commencement of the next 
week the funds had been obtained to pay these, and to double their number. In six weeks 
not less than one hundred hands were at work on the hill-top and in the city. Mechanics 
of all trades subscribed for stock, and paid their subscription in work. The stone of which 
the building is erected was quarried from the grounds of the society. The lime was burnt on 
the hill, and every means was adopted to reduce the necessary expenditure. Payment for 
stock in the society was received in every possible article of trade; due-bills wer^ taken, and 
these were converted into others which would serve in the payment of bills. 

In this way the building was reared, and finally covered in, without incurring any debt. 
But the conditions of the bonds by which the lot of ground was held required the completion 
of the observatory in two years from its date; and these two years would expire June, 1845. 
It was seen to be impossible to carry forward the building fast enough to secure its comple- 
tion by the required time, without incurring some debt. My own private resources were 
used, in the hope that a short time after the finishing of the observatory would be sufficient 
to furnish the funds to meet all engagements. The work was pushed rapidly forward. In 
February, 1845, the great telescope safely reached the city of Cincinnati; and in March the 
building was ready for its reception. I had now exhausted all my private means, and to in- 
crease the difficulty of the position in which I was placed, the college edifice took fire and 
burned to the ground. My ordinary means of support were thus destroyed at a single blow. 
I had engaged to conduct the observatory, without compensation from the society, for ten 
years, in the hope that my college salary would be sufficient for my wants. It was impossi- 
ble to abandon the observatory. The college could not be rebuilt, at least for several years, 
and in this emergency I found it necessary to seek some means of support, least inconsist- 
ent with my duties in the observatory. My public lectures at home had been comparatively 
well received, and after much hesitation it was resolved to make an experiment elsewhere. 
For five years I had been pleading the cause of science among those little acquainted with 
its technical language. I had become habituated to the use of such terms as were easily 
understood; and probably to this circumstance, more than to any other one thing, am I in- 
debted for any success which may have attended my public lectures. To the citizens of 
Boston, Brooklyn, New York, and New Orleans, for the kindness with which they were 
pleased to receive my imperfect efforts, I am deeply indebted. My lectures were never 
written, and no idea was entertained of publishing a course, until the partiality of my friends 
induced me to attempt this experiment. 

Such are the circumstances under whl?h this effort to trace the career of the human 
mind, in its researches among the stars, h i been undertaken. No one science, perhaps, so 



• PBMFAC3. 

perfectly illustrates the gradual growth and development of the powers ui numan genius. 
The movement of the mind has been constantly onward — its highest energies have ever been 
called into requisition — and there never has been a time when astronomy did not present 
problems not only equal to all that man could do, but passing beyond the limits of hig 
greatest intellectual vigor. Hence, in all ages and countries, the absolute strength of hu- 
man genius may be measured by its reach to unfold the mysteries of the stars . 

It will be seen that in the following lectures one single object has engaged the attention of 
the writer, — the structure of the universe, so far as revealed by the mind of man. The uses 
of science have in no way been considered. The effects on the mind, on society, on civiliza- 
tion, on commerce, on religion, have not been permitted to mar the unity of the original 
design. The onward, steady, triumphant march of mind, in its study and exploration of 
the universe of God has been my only object, the single theme of the entire series. 

Cincinnati Observatory, 
Mount Adams, May, 1848. 



THE STRUCTURE OF THE UNIVERSE 



INTRODUCTORY LECTURE. 

AH EXPOSITION OF THE PROBLEM WHICH THE HEAVENS PRESENT 

FOB SOLUTION. 

The subject to which your attention is inrited, claims no specific con- 
nection with the every-day struggle of human life. Far away from the earth 
on which we dwell, in the blue ocean of space, thousands of bright orbs, 
in clusterings and configurations of exceeding beauty, invite the upward 
gaze of man, and tempt him to the examination of the wonderful sphere by 
which he is surrounded. The starry heavens do not display their glittering 
constellations in the glare of day, while the rush and turmoil of business in- 
capacitate man for the enjoyment of their solemn grandeur. It is in the 
stillness of the midnight hour, when all nature is hushed in repose, when 
the hum of the world's on-going is no longer heard, that the planets roll 
and shine, and the bright stars, trooping through the deep heavens, speak 
to the willing spirit that would learn their mysterious being. 

Often have I swept backward in imagination six thousand years, and 
stood beside our Great Ancestor, as he gazed for the first time upon the 
going down of the sun. What strange sensations must have swept through 
his bewildered mind, as he watched the last departing ray of the sinking 
orb, unconscious whether he should ever behold its return. Wrapt in a 
maze of thought, strange and startling, his eye long lingers about the point 
at which the sun had slowly faded from his view. A mysterious darkness, 
hitherto unexperienced, creeps over the face of nature. The beautiful 
scenes of earth, which through the swift hours of the first wonderful day 
of his existence, had so charmed his senses, are slowly fading one by one 
from his dimmed vision. A gloom deeper than that which covers earth, 
steals across the mind of earth's solitary inhabitant. He raises his inq ilt- 
ing gaze towards heaven, and lo ! a silver crescent of light, clear and beauti- 
ful, hanging in the western sky, meets his astonished eye. The young 
moon charms his untutored vision, and leads him upward to her bright 
attendants, which are now stealing one by one, from out the deep blue sky. 



& eTRtjerms of tbb univerbb. 

The solitary gazer bows, and wonders, and adores. The hours glide by— 
the silver moon is gone- Uie stars are rising— slowly ascending the heights 
of heaven — and solemnly sweeping town ward in the stillness of the night. 
The first grand revolution to mort**l vision is nearly completed. A faint 
streak of rosy light is 3een in the east — it brightens — the stars fade — the 
planets are extinguished — the eye is fixed in mute astonishment on the 
growing splendor, till the first rays of the returning sun dart their radiance 
on the young earth and its solitary inhabitant. To him "the evening and 
the morning were the first day." 

The curiosity excited on this first sole na night — the consciouness that in 
the heavens God had declared his gloty -the eager desire to comprehend 
the mysteries that dwell in these bright irbs, have clung to the descendants 
of him who first watched and wondered, fhrough the long lapse of six thou- 
sand years. In this boundless field of investigation, human genius has won 
its most signal victories — Generation after generation has rolled away, age 
after age has swept silently by, but each has swelled by its contributions 
the stream of discovery — One barrier after another has given away to the 
force of intellect — mysterious movements have been unravelled — mighty 
laws have been revealed — ponderous orbs have been weighed, their reciprocal 
influences computed, their complex wanderings made clear, until the mind, 
majestic in its strength, has mounted step by step up the rocky height of 
its self-built pyramid, from whose star-crowned summit it looks out upon the 
grandeur of the universe, self -clothed with the prescience of a God. — With 
resistless energy it rolls back the tide of time, and lives in the configuration 
of rolling worlds a thousand years ago, or more wonderful, it sweeps away 
the dark curtain from the future, and beholds those celestial scenes which 
shall greet the vision of generations when a thousand years shall have rolled 
away, breaking their noiseless waves on the dim shores of eternity. 

To trace the efforts of the human mind in this long and ardent struggle, 
to reveal its hopes and fears, its long years of patient watching, its moments 
of despair and hours of triumph — to develop the means by which the deep 
foundations of the rock-built pyramid of science have been laid, and to fol- 
low it as it slowly rears its stately form from age to age, until its vertex 
pierces the very heavens — these are the objects, proposed for accomplish- 
ment and these are the topics to which I would invite your earnest attention. 
The task is one of no ordinary difficulty. It is no feast of fancy, with music 
and poetry, with eloquence and art, to enchain the mind. Music is here — 
but it is the deep and solemn harmony of the spheres. Poetry is here — but 
it must be read in the characters of light, written on the sable garments of 
night. Architecture is here — but it is the colossal structure of sun and 
system, of cluster and universe. Eloquence is here — but " there is neither 
speech nor language — Its voice is not heard," yet its resistless sweep 
comes over us in the mighty periods of revolving worlds. 

Shall we not listen to this music, because it is deep and solemn? Shall 



INTRODUCTORY LBOTUBB. 18 

we not read this poetry, because its letters are the stars of heaven ? — Shatt 
we refuse to contemplate this architecture, because " its architraves, its 
archways, seem ghostly from infinitude ? " Shall we turn away from this 
surging eloquence, because its utterance is made through sweeping worlds ? 
No — the mind is ever inquisitive, ever ready to attempt to scale the most 
rugged steeps. Wake up its enthusiasm — fling the light of hope on its path- 
way, and no matter how rough and steep and rocky it may prove, onward } 
is the word which charms its willing powers. 

It is not my wish or design to introduce you to the dark technicalities of 
science, neither do I propose to rest satisfied with the barren statement of 
the results which have been reached by the efforts of genius. While on 
the one hand I shall endeavor to shun all attempt at critical scientific 
demonstration, which could only be intelligible to the professed student of 
astronomy, I shall on the other hand fearlessly attempt such an exposition 
of the processes and trains of reasoning by which great truths have been 
elicited, as to show to every intelligent mind that the problem is not im- 
possible ; by simplicity of language, by familiar illustrations, to fling 
light enough upon these mysterious propositions, to show a pathway, 
though it be dim and rugged, still a pathway, which if pursued shall cer- 
tainly lead to a full and perfect solution. I ask, then, no critical previous 
knowledge of the subject, on the part of those who would follow me in the 
wonderful developments which I am aboutto attempt. Give me but your 
earnest and unbroken attention. Go with me in imagination, and join 
in the nightly vigils of the astronomer, and while his mind with powerful 
energy struggles with difficulty, join your own sympathetic efforts with 
his — hope with his hope — tremble with his fears — rejoice with his triumphs. 
Lend me but this kind of interest, and my task is already half accom- 
plished. 

Before proceeding to an actual exposition of the structure of the 
Heavens, I propose in this introductory lecture to announce the nature 
of the problem, which the mind has essayed to resolve, and to point out 
the more important auxiliaries, mental and mechanical, which it has con- 
jured to its aid. If the difficulties of this problem should overwhelm the 
miud, let it be remembered that the astronomer has ever lived, and never 
dies. The sentinel upon the watchtower is relieved from duty, but another 
takes his place, and the vigil is unbroken. No — the astronomer never 
dies. He commences his investigations on the hill tops of Eden — he 
studies the stars through the long centuries of antediluvian life. The 
deluge sweeps from the earth its inhabitants, their cities and their monu- 
ments — but when the storm is hushed, and the heavens shine forth in 
beauty, from the summit of Mount Ararat the astronomer resumes his 
endless vigils. In Babylon he keeps his watch, and among the Egyptian 
priests he inspires a" thirst for the sacred mysteries of the stars. The 
plains of Shinar — the temples of India — the pyramids of Egypt, are equally 



U MfBUOTURS OF TME VNIVER8K 

Mi watching places. When science fled to Greece, his home was la 
the schools of her philosophers ; and when darkness covered the earth for 
a thousand years, he pursues his never-ending task from amidst the burn 
ing deserts of Arabia. When science dawned on Europe, the astronomer 
was there — -toiling with Copernicus — watching with Tycho — suffering 
with Galileo — triumphing with Kepler. Six thousand years have rolled 
away since the grand investigation commenced. We stand at the 
terminus of this vast period, and looking back through the long vista of 
departed years, mark with honest pride the successive triumphs of our 
race. Midway between the past and future, we sweep backward and 
witness the first rude effort to explain the celestial phenomena — we may 
equally stretch forward thousands of years, and although we cannot com- 
prehend what shall be the condition of astronomical science at that remote 
period, of one thing we are certain — the past, the present, and the future, 
constitute but one unbroken chain of observations, condoning all time, to- 
the astronomer, into one mighty now. 

From the vantage ground which we occupy, it will not be difficult to 
announce so much of the great problem as has already been resolved, and 
to form some approximate conception of what remains for future ages to 
accomplish. 

In the exposition about to be attempted, I do not propose to present any 
trains of reasoning, or any results which may have been reached. These 
shall engage our attention hereafter. At present permit me simply to trans- 
late into language the questions which the visible heavens propound. 

The most cursory examination of the celestial vault reveals the fact, that 
not one solitary object, visible to the eye, is at rest. Motion is the attribute 
of sun and moon and planets and stars. The earth we inhabit alone re- 
mains fixed, to the senses. 

The first great problem propounded for human Ingenuity, is to sever real 
motion from that which is unreal and only apparent. To accomplish this, 
some knowledge of the form of the earth which we inhabit must be ob- 
tained. Not only must we acquire a knowledge of its figure, but in like 
manner we must learn with certainty its actual condition, whether of rest 
or motion. If at absolute rest in the center of the universe, then the rising 
sun, the setting moon, the revolving heavens, are real exhibitions, and 
must be examined as such. On the contrary, should it be found to be im- 
posible to predicate of the earth absolute immobility, then arises the com- 
plicated question, how many motions belong to it ? and with what velocity 
does it move ? If a motion of rotation exist, what is the position of the 
axis about which it revolves, and is this axis permanent or changeable ? 
If a motion of translation in space must be adopted, then whither is the 
earth urging its flight? what the nature of the path described? the 
Telocity of its movement, and the laws by which it is governed ? Theee 
are some of the questions which present themselves in the outset, touching 



UTTBODTTCTOBY LECTUBB. \ 

the condition of the earth, on whose surface the astronomer is located, in 
his researches of the heavens. 

Beyond the limits of the earth, a multitude of objections present them- 
selves for examination: and first of all the sun, the great source of life and 
light and heat, demands the attention of the student of the heavens. That 
some inscrutable tie binds it to the earth, or the earth to it, wag early 
recognized in the fact, that whether the sun was moving or at rest, the rela- 
tive distance of it and the earth never changed by any great amount ; and 
whatever changes did occur, were all obliterated in a short period, and the 
distance by which these bodies are separated was restored to its primitive 
value, to recommence its cycle of changes in the same precise order. — Here 
then was a grand problem, to determine the relations existing between the 
sun and earth ; to endue with motion that one of these bodies which did 
move, and to fix the limits within which the observed changes occurred, 
both in time and distance. 

While the connection between the sun and earth was certain, a mutual 
dependence between the earth and the other great source of light, the moon, 
was equally manifest. The invariability in the apparent diameter of the 
moon, demonstrates the fact, that whether the earth were moving or sta- 
tionary, the moon never parts company with our planet. In all her wander- 
ings among the fixed stars, in her elongations from the sun, in her wond- 
rous phases and perpetual changes, some invisible hand held her at the 
same absolute distance from the earth. But to decide whether this power 
resided in the earth or the moon, or in both, to explain these wondrous 
changes from the silver crescent of the western sky to the full orb which 
rose with the setting sun, pouring a flood of light over all the earth, to de- 
velop the mysterious connection between the disappearance of the moon 
and those terrific phenomena, the going out of the sun in dim eclipse — 
these furnished themes for investigation requiring long centuries of patient 
watching of never-ending toil. 

Passing out from the sun and moon to the more distant stars, among the 
brightest of those which gemmed the nocturnal heavens, a few were found 
differing from all the rest in the fact that they wandered from point to point, 
and at the end of intervals widely differing among themselves, swept round 
the entire heavens, and returned to their starting point, to recommence 
their ceaseless journies. These were named planets wanderers, in contradis- 
tinction to the host of stars which were fixed in position, unchanged from 
century to century. 

Hence arose a new and profound series of investigations : where were 
these wandering stars urging their flight ? Were their motions real or 
apparent ? Were their distanees equal or unequal ? Did any tie bind 
tk«m to the earth, or to the sun, or to each other ? Were their distances 
from the earth eons^ant or variable ? Were their motions irregular, or 
glided by law ? Did they awomplkh their reyoluticmi ameng the £x®d 



16 & GTUBE OF THE UNIVERSE. 

stars in regular curves, or in lawless wanderings ? Among all the moving 
bodies, sun, moon, and planets, could any principle of association be traced 
which might bind them together and form them into a common system ? 

To resolve these profound questions, a critical watch is kept on all the 
moving bodies. Their pathway is among the stars, and to these ever during 
points of light their positions are constantly referred. If beyond the limits 
of the moving bodies a dark veil had been drawn so as to have excluded 
the light of the stars, at the first glance it might seem that by such a change, 
simplicity would have been introduced, and the perplexity arising from the 
motion of the planets among the profusely scattered stars, would have been 
removed. 'But let us not judge too hastily. Blot out the stars, and give 
to the sun, moon and planets a blank heavens in which to move, and the 
possibility of unraveling their mysterious motions, mutual relations, and 
common laws, is gone forever. 

This will become manifest when we reflect that on such a change, not a 
fixed point in all the heavens would remain, to which we could refer a 
moving planet. They must then be referred to each other, and the motion 
due to the one, would become inextricably involved in that due to the other, 
and neither could be determined with any precision. Like the ocean isl- 
ands which guided the early mariners, so God has given to us the stars of 
heaven as the fixed points to which we can ever refer, in all parts of their 
revolutions, the places of the wandering planets, and the swiftly revolving 
moon. 

As the necessity for accuracy in watching the movements of the planets 
became more apparent, the attention was directed to the acquisition of 
the means by which this might be accomplished. Hence we find in the 
earliest ages the astronomer grouping the fixed stars into constellations — 
breaking up the great sphere of the heavens into fragments, the more easily 
to study its parts in detail. Not only are the stars of each constellation 
numbered, their brilliancy noted, but their relative places in the constella- 
tion and to each other, are fixed with all the precision which the rude 
means then in use permitted. Names are fixed to these different group- 
ings, when or where or by whom we know not. Neither history nor tra- 
dition lead us back to this first breaking up of the heavens, but the names 
then bestowed on the fragmentary parts, the richer constellations, have sur- 
vived the fall of empires, and are fixed forever in the heavens. 

Possessing now a thorough knowledge of the objects among which the 
planets were moving, and the means of measuring with approximate ac- 
curacy, their distance from the stars along their path, it became possible 
to trace a planet in its career, and to note the changes of its velocity. New 
and wonderful discoveries were thus made. It was found that all the 
planets moved with an irregular velocity. Sometimes swiftly advancing 
among the fixed stars, then slowly relaxing their speed, they actually stop- 
ped, tamed backward in their career, stopped again, and then, at first 



INTRODUCTORY LECTURE. i7 

slowly but afterwards more rapidly, resumed their onward motion. These 
strange and anomalous motions, differing from anything remarked in the 
sun and moon, furnished new themes for discussion, new problems for solu- 
tion. While the phenomena above alluded to became known, the same chain 
of observations revealed the remarkable fact, that the periods of revolution 
of the planets, though differing for each one of the group, were identical 
for any one individual, and moreover, that a simple curve marked out the 
pathway of sun, moon and planets, among the fixed stars, and that all these 
wandering bodies were confined to a narrow zone or belt in the heavens. 
Centuries had now rolled away, nay, even thousands of years had slowly 
glided by, since the mind had first given itself to the examination of the 
heavens, and while discovery after discovery had rewarded the zeal of the 
observer in every age, yet the grand object of research, the distinction be- 
tween actual and apparent motion, had thus far eluded the utmost efforts 
of human genius. But a brighter day was dawning. Each successive 
effort tore away some petty obstruction which impeded the march of mind 
upward towards the lofty region of truth. Facts grew and multiplied. 
Phenomena striking and diversified, were collated and compared. The 
mind in imagination took leave of the earth as the centre of all these com- 
plex movements, inexplicable on its surface, and naturally urged its flight 
towards the sun. There it paused and rested, and from this fixed point 
looked out upon the circling orbs, andlo ! the complexity of their movements 
melted away. The centre was found — the mystery solved — the ponderous 
earth rescued from its false position, rolled in its place among the planets, 
one of the great family that swept in beauty and harmony about their com- 
mon parent the sun. 

The mind now stood upon the first platform of the rocky pyramid which 
it had been slowly rearing and with which it had been slowly rising, through, 
long centuries of ceaseless toil. One grand point had been gained. Dark- 
ness had given way to light, but the great problem of the universe was yet 
to be resolved. All this long and arduous struggle had only revealed what 
the problem was. Appearances were now separated from realities, and 
with a fresh and invigorated courage the human mind now gives its ener- 
gies to the accomplishment of definite objects, no longer working uncer- 
tainly in the dark, but with the clear light of truth to guide and conduct 
the investigation. 

' Possessed of these extraordinary advantages, the advance now became 
rapid and brilliant, as it had previously been slow and discouraging. That 
the planets, reckoning the earth as one, constituted a mighty family of 
worlds, was now manifest — whether linked singly to the sun, or mutually 
influencing each other, was the grand question. This great problem rested 
■upon the resolution of a multitude of subordinate ones. The actual eurve 
constituting the planetary orbits, the magnitude of these orbits, their actual 
position in spaee, the values and directions of their principal lines, the lawi 



18 STRUCTURE OF THE UNIVERSE. 

of their motion, all these and many more questions of equal importance 
and intricacy presented themselves in the outset of the examination now 
fairly commenced. Human skill was exhausted in the contrivance and 
construction of mechanical aids by which the movements of the planets 
might be watched with the greater accuracy. Partial success crowned 
these extraordinary efforts, but there yet remained delicate investigations 
which with the utmost skill in observing escaped the farthest reach of 
man's eagle gaze, and seemed to bid defiance, to all his powers. 

To conquer these difficulties, one of two things must be accomplished : 
either man must sweep out from earth towards the distant planets, to gain 
a nearer and more accurate view, or else bring them down from their lofty 
spheres to subject themselves to his scrutinizing gaze. How hopeless the 
accomplishment of either of these impossible alternatives. But who 
shall prescribe the limits of human genius ? In studying the phenom- 
ena of the passage of light through transparent crystalized bodies, a 
principle is discovered which lets in a gleam of hope on the disheartened 
mind. It seizes this principle, converts it to its use, and arms itself with 
an instrument more wonderful than any that fancy in its wildest dreams ever 
pictured to the imagination. With the potent aid of this magic instru- 
ment, the astronomer no longer is bound hopelessly to his native earth ; 
without indeed quitting in person its surface, his eye gifted with super- 
human power, ranges the illimitable fields of space. He visits the moon, 
and finds a world with its lofty mountains and spreading" valleys. The 
star-like planets swell into central worlds, with their circling moons, and 
myriads of fixed stars, hitherto beyond the reach of human vision, stand 
revealed in all their sparkling beauty. It is as if the united ranges of a 
thousand eyes were all concentrated in a single one. 

A new era now dawns on the world. The delicate and invisible Irregu- 
larities of the planetary motions are now fully revealed, and the data rap- 
idly accumulate by means of which the last grand question is to be re- 
solved. The orbitual curves are determined. The laws of the revolving 
planets are revealed. A mysterious relation between the distances of the 
planets from the sun and their periods of revolution unites them positively 
into one grand family group. That they are bound to the sun by some in- 
scrutable power, is certain, and it now remains to determine the law of in- 
crease and decrease of this force for all possible distances. This last truth 
is finally achieved, and the wisdom of God is vindicated in the beautiful 
structure of our grand system. 

The second lofty platform is reached in the mighty pyramid, whose 
summit is now nearing the stars of heaven. From this elevation the mind 
looks out upon the circling planets and their revolving satellites, and the 
mysterious eomet, and ventures to propound the question, do these bodies 
so interfere with the movements of each other, as to effect permanently 
tha structure by which the equilibrium and stability of the entire system 
is guarantied ? 



INTRODUCTORY LECTURE. 19 

To answer this question, a new train of investigation is commenced, 
satellite is weighed against planet, and planet against the sun, until the mass 
of matter contained in each individual of the system becomes accurately 
known. Then is undertaken the grand problem of perturbations. The tele- 
scope reveals the fact that slow and mysterious changes are going on in 
the mean motions of the moon, in the figure of the planetary orbits, and 
in the relative positions which these orbits hold to each other. Are these 
change ever progressive? If this be true, then, does the system contain 
within itself the seeds of decay, the elements of its own destruction. 
Slowly but surely as the solemn tread of time, the end must come, and one 
by one planet and satellite and comet, sink forever in the sun. Long 
and arduous was the struggle to reach the true answer to this difficult 
question. The entire solution involved a multitude of parts. 

When the mutual dependence of the multitude of bodies constituting 
our system was discovered, when planet, and satellite, and comet, were 
found to feel and sway to the influence which each exerted on the other, 
the simplicity of their movements was gone forever ; orbits once fixed 
in the heavens, slowly swung away from their moorings ; the beautiful 
precision which had to all appearance marked the planetary curves, was 
destroyed. The regularity of their motions was changed into irregularity 
and a system of complexity which seemed to bid defiance to all effort at 
comprehension, presented itself to the human intellect. 

It was no less than this — given, a system of revolving worlds, mutually 
operating on each other ; required, their magnitude, masses, distances, 
motions, and positions, at the close of a thousand revolutions. What 
mind possessed the gigantic power to grasp this mighty problem ? 
Reason was lost in wandering mazes, and the brightest intellect sunk cloud- 
ed in gloom. 

In this dilemma, the mind turns inward on its own resources. As the 
physical man climbs some mountain height by successive efforts, rising 
higher and higher, scaling rock after rock, and mounting precipice after 
precipice, by the use of strength comparatively feeble, resting and re- 
cruiting as it becomes exhausted, was it impossible, to contrive some mental 
machinery which might give to the reason the power of prosecuting its 
difficult researches, in such manner that it might stop and rest and not 
lose what it had already gained in its onward movement ? 

Geometry had invigorated the reason, as exercise toughens and strength- 
ems the muscles of the human frame. But it had given to the mind no 
mechanical power, wherewith to conquer the difficulties which rose su- 
perior to its natural strength. Archimedes wanted but a place whereon to 
stand, and with his potent lever he would lift the world. The astronomer 
demands an analogous mental machinery to trace out the complex wander- 
ings of a system of worlds. What the human mind demands and resolves 
to find, it never fails to discover. The infinitesimal analysis is reached, 



20 STRUCTURE OF TRE UNIVERSE. 

its principles developed* its resistless power, compelled into the service of 
human reason. I shall not now stop to explain the nature of this analysis. 
Its power and capacity alone engage our attention at the present. Once 
having seized on a wandering planet, it never relaxes its hold, no matter 
how complicated its movements, how various the influences to which it 
may be subjected, how numerous its revolutions, no escape is possible. 
This subtle analysis clings to its object, tracing its path and fixing its 
place with equal ease, at the beginning, middle, or close of a thousand rev- 
olutions, though each of these should require a century for its accomplish 
ment. 

Armed with this analysis, which the mind had created for its use, giving 
to it a strength only commensurate with the increased power which had 
been given to the human eyes, it concentrated its energies once more up- 
on this last greatest problem. One by one these strongholds give way, 
the resistless power of analysis marches onward from victory to victory, 
until finally the sublime result is reached, the system is stable, the 
equilibrium is perfect ; slowly rocking to and fro in periods which stun 
the imagination, the limits are prescribed beyond which these fluctuations 
shall never pass. 

Here it would seem that human ambition might rest. Satisfied with 
having mastered the mysteries of the system with which we are united, the 
mind might cease its arduous struggle, and leave the wilderness of fixed 
stars free from its intrusions and ceaseless persecutions. But this is not 
the effect produced by victory ; success but engenders new desires, and 
prompts to more difficult enterprises. Man having obtained the mastery 
over his own system, boldly wings his flight to the star-lit vault, and re- 
solves to number its countless millions, to circumscribe its limitless 
extent, to fathom its infinite depth, to fix the centre about which his in- 
numerable host is wheeling its silent and mysterious round. 

Here commences a new era. The first step in the stupendous enterprise 
is to determine the distance of some one fixed star. Here again the mind 
is long left to struggle with difficulties which it seemed that no ingenuity 
or skill could remove. But its efforts do not go unrewarded. If it fails 
in the accomplishment of its grand object, it is rewarded by the most 
brilliant discoveries. The mighty law governing the planetary worlds is 
extended to the region of the fixed stars, motion is there detected, orbitual 
motion, the revolution of sun about sun. The swift velocity of light is 
measured, to become the future unit in the expression of the mighty dis- 
tances which remain yet to be revealed. Ever baffled but never con- 
quered, the mind returns again and again to the attack, till finally the 
problem slowly yields, the immeasurable gulf is passed, and the distance 
of a single star rewards the toils of half a century. But what a triumph 
is this ? It is no less than a revelation of the scale on which the universe 
is built. The interval from sun to fixed stars, is that by which the stars 



UrmODUCTOET LSCTTTRK 21 

we separated ; and a reach of distance is opened up to the mind, which 
it only learns to contemplate by long continued effort. 

But another startling fact is revealed in the prosecution of these pro- 
found investigations. The minute examinations of the fixed stars, have 
changed their character. For thousands of years they had been regarded 
as absolutely fixed among each other. This proves to be mere illusion, 
resulting from the use of means inadequate for the determination of their 
minute changes. Under the scrutinizing gaze of the eye, with its power 
increased a thousand-fold, the millions of shining orbs which fill the 
heavens, are all found to be slowly moving around each other, slowly as 
seen from our remote position, but with amazing velocity when examined 
near at hand. 

A new problem of surprising grandeur now presents itself. Are these 
motions real ? or are they due to a motion in the great centre of our sys- 
tem ? A series of examinations analogous to those which divided between 
the real and apparent motions in the planets, is commenced and prosecut- 
ed with a zeal and devotion unsurpassed in the history of science. The 
mind rises to meet the sublime investigation. For a hundred years it toils 
on ; again it triumphs ; the truth is revealed. The immobility of the sun 
is gone forever ; our last fixed point is swept from under us, and now the 
entire universe is in motion. 

With redoubled energy the mind still prosecutes the inquiry, whither 
is the sun sweeping, and with what velocity does it pursue its unknown 
path ? Strange and incredible as it may appear, these questions are an- 
swered ; and in attaining this answer, the means are reached to separate 
between the real and apparent motions of the fixed stars, and to study 
their complex changes, and to rise by slow degrees, to a complete knowl- 
edge of the movements of the grand sidereal system. Here we pause. 
Rapidly have we descended the current of astronomical research, we have 
attained the boundary of the known. "We stand on the dim confines of 
the unknown. All behind us is clear and bright and perfect, all before us 
is shrouded in gloom and darkness and doubt. Yet the twilight of the 
known flings its feeble light into the domain of the unknown, and we are 
permitted to gather some idea, not of all that remains to be done, but of 
that which must be first accomplished. 

Let us then stretch forward and propound some of those questions which 
nature yet presents for solution, but which have hitherto resisted the efforts 
of the human mind. First of all, we begin with our own system. How 
came it to be constituted as it actually exists? All the analogies of nature 
forbid the idea that it was thus instantly called into being by the fiat of 
Omnipotence. Does it come, then, from some primitive modification of 
matter, under the action of laws working out their results in eountless 
millions of ages ? Who shall present the terue cosmogony of the solar sys- 



22 STBVCTTJER OF THE UNtVEBSS. 

But this is only one unit among many millions. Whence the myriads 
of stars ? those stupendous aggregations into mighty clusters ? what the 
laws of their wonderful movements, of their perpetual stability? Who 
will explain the periodical stars, that wax and wane, like the changing 
moon : or still more wonderful, reveal the mystery of those which have 
suddenly burst on the astonished vision of man, and have as suddenly gone 
out forever in utter darkness. 

Such are the questions which remain for the resolution of future ages. 
We may not live to witness these anticipated triumphs of mind over mat* 
ter ; but who can doubt the final result? Look backward to the Chaldean 
shepherd, who watched the changing moon from the plains of Shinar, and 
wondering, asked if future generations would reveal those mysterious 
phases? Compare his mind and knowledge with those of the modern 
astronomer, who grasps at a single glance, the past, present, and future 
changes of an entire system. Are the heights which remain to be reached, 
more rugged, more inaccessible, than those which have been already so 
triumphantly scaled ? The observations recorded in Babylon three thou- 
sand years ago, have reached down through the long series of centuries, 
and are of inestimable value, in the solution of some of the darkest prob- 
lems with which the mind has ever grappled. In like manner, the rec- 
ords we are now making, shall descend to unborn generations, and con- 
tribute to effect the triumphs of genius when three thousand years shall 
have rolled away. If doubt arises as to the final resolution of these pro- 
found questions, from the immense distance of the objects under examina- 
tion, let us call to mind the fact, that the artificial eye which man has fur- 
nished for his use, possesses a glance so piercing, that no distance can hide 
an object from his searching vision. 

Should Sirius, to escape this fiery glance, dart away from its sphere, and 
wing its flight at a velocity of twelve millions of miles in every minute, for 
a thousand years ; nay, should it sweep onward at the same speed for ten 
thousand years, this stupendous distance cannot bury it from the persecut- 
ing gaze of man. But if distance is to form no barrier, no terminus to 
these investigations, surely there is one element which no human ingenuity 
can overcome. The complex movements of the planetary orbs have been 
revealed, because they have been repeated a thousand times under the eye 
of man, and from a comparison of many revolutions, the truth has been 
evolved. But tens of thousands of years must roll away before the most 
swiftly moving of all the fixed stars shall complete even a small fragment 
of its mighty orbit. With motions thus shrouded, these would seem to be 
in entire seourity from the inquisitive research of a being whose whole 
sweep of existence is but a moment, when compared with these vast 
periods. But let us not judge too hastily. The same piercing vision that 
follows the retreating star to depths of space almost infinite, is armed with 
a power so great, that if this same star should commence to revolve around 



INTRODUCTORY LECTURE. -J3 

some grand centre, and move so slowly that five millions of years must 
roll away before it can complete one circuit, not even a single year shall 
pass before its motion shall be detected, in ten years its velocity shall be 
revealed, and in the life-time of a single observer its mighty period shall 
become known. 

If human genius is not to be baffled either by distance or time, numbers 
shall overwhelm it, and the stars shall find their safety in their innumer- 
able millions. This retreat may even fail. The watch towers of science 
now cover the whole earth, and the sentinels never sleep. No star or 
cluster or constellation, can ever set. It escapes the scrutinizing gaze of 
one astronomer, to meet the equally piercing glance of another. East and 
west and north and south, from the watch towers of the four quarters of 
the globe, peals the solemn mandate, onward! 

Here we pause. We have closed the enunciation of the great problem 
whose discussion and solution lie before us, a problem whose solution has 
been in progress six thousand years — one which has furnished to man the 
opportunities of his loftiest triumphs, one which has taxed in every age the 
most vigorous efforts of human genius, a problem whose successive develop- 
ments have demonstrated the immortality of mind and whose sublime re- 
sults have vindicated the wisdom and have declared the glory of God. You 
have listened to the enunciation, we now invite you to follow us in the de- 
monstration. And may that Almighty power, which built the heavens, 
gave to me wisdom to reveal, and to you power to grasp the truths and doc- 
trines, wrested by mind from nature in its long struggle of sixty centuries 

•i tea i 



LECTURE IX. 

THE DISCOVERIES OP THE PRIMITIVE AGES. 

To those who have given but little attention to the science of astronomy, 
its truths, its predictions, its revelations, are astonishing ; and but for their 
rigorous verification, would be absolutely incredible. When we look out 
upon the multitude of stars which adorn the nocturnal heavens, scattered in 
bright profusion in all directions, without law, and regardless of order — when 
with telescopic aid, thousands are increased to millions, and suns . and 
systems and universes, rise in sublime perspective, as the visual ray sweeps 
outwards to distances which defy the powers of arithmetic to express, how 
utterly futile does it seem, for the mind to dare to pierce and penetrate, to 
number, weigh, measure and circumscribe, these innumerable millions? It 
is only when we remember, that from the very cradle of our race, strong and 
powerful minds, have in rapid and continuous succession, bent their en- 
ergies upon the solution of this grand problem, that we can comprehend, 
how it is, that light now breaks in upon us, from the very confines of the 
universe, dimly revealing the mysterious forms, which lie yet half concealed 
in the unfathomable gulfs of space. When I reflect on the recent truimphs 
of human genius — when I stand on the shore of that mighty stream of dis- 
covery, which has grown broader and deeper, as successive centuries have 
rolled away, gathering in strength and intensity, until it has embraced the 
whole universe of God ; I am carried backward through thousands of years, 
following this stream, as it contracts towards its source, till finally its silver 
thread is lost in the clouds and mists of antiquity. I would fain stand at the 
very source of discovery, and commune with that unknown god-like mind 
which first conceived the grand thought, that even these mysterious stars 
might be read, and that the bright page which was nightly unfolded to the 
vision of man, needed no interpreter of its solemn beauties, but human 
genius. There is to my mind, no finer specimen of moral grandeur, than 
that presented by him who first resolved to read and comprehend the heav- 
ens. On some lofty peak he stood, in the stillness of the midnight hour, 
with the listening stars as witnesses of his vows, and there, conscious of 
his high destiny, and of that of his race, resolves to commence the work of 
ages. " Here," he exclaims, " is my watch-tower, and yonder bright orbs, 
are henceforth my solitary companions. Night after night, year after year, 
will I watch and wait, ponder and reflect, until some ray shall pierce the 
deep gloom which now wraps the world." 

Thus resolved the unknown founder of the science of the stars. Hi* 



26 STRUCTURE OF THE UmVERaS, 

name and his country are lost forever. What matters this, since his works, 
his discoveries, have endured for thousands of years and will endure, as 
long as the moon shall continue to fill her silver horn, and the planets to 
roll and shine. 

Go with me, then, in imagination, and let us stand beside this primitive 
observer, at the close of his career of nearly a thousand years, (for we must 
pass beyond the epoch of the deluge, and seek our first discoveries among 
those sages, whom, for their virtues, God permitted to count their age, 
not by years, but by centuries,) and here we shall learn the order in which 
the secrets of the starry world slowly yielded themselves, to long and per- 
severing scrutiny. And now let me unfold, in plain, and simple language, 
the train of thought, of reasoning and research, which marked this primi- 
tive era of astronomical science. It is true that history yields no light, and 
tradition even fails, but such is the beautiful order in the golden chain of 
discovery, that the bright links which are known, reveal with certainty, 
those which are buried in the voiceless past. — If then it were possible to 
read the records of the founder of astronomy, graven on some column of 
granite, dug from the earth, whither it had been borne by the fury of the 
deluge, we know now what its hieroglyphics would reveal, with a certainty 
scarcely less than that which would be given by an actual discovery, such 
as we have imagined. We are certain that the first discovery ever recorded, 
as the result of human observation, was on the moon. 

The sun, the moon, the stars, had long continued to rise, and climb the 
heavens, and slowly sink beneath the western horizon. The spectacle of 
day and night, was then as now, familiar to every eye ; but in gazing there 
was no observation, and in mute wonder there was no science. When the 
solitary observer took his post, it was to watch the moon. Her extraordinary 
phases had long fixed his attention. Whence came these changes ? The 
sun was ever round and brilliant — the stars shone with undimmed splendor 
— while the moon was ever waxing and waning, sometimes a silver crescent 
hanging in the western sky, or full orbed, walking in majesty among the 
stars, and eclipsing their radiance, with her overwhelming splendor. 
Scarcely had the second observation been made upon the moon, when 
the observer was struck with the wonderful fact, that she had left her 
place among the fixed stars, which on the preceding night he had accurately 
marked. Astonished, he again fixes her place by certain bright stars 
close to her position, and waits the coming of the following night. His 
suspicions are confirmed — the moon is moving ; and what to him is far 
more wonderful, her motion is precisely contrary to the general revolution 
of the heavens, from east to west. With a curiosity deeply aroused, he 
watches from night to night, to learn whether she will return upon her 
track ; but she marches steadily onward among the stars, until she sweep* 
the entire circuit of the heavens, and returns to the point first occupied, to 
recommence her ceaseless cycles. 



THE DISCOVERIES OF THE PRIMITIVE AGES, 27 

An inquiry now arose, whether the changes in the moon, her increase and 
decrease, could in any way depend on her place among the fixed stars. To 
solve this question required a longer period. The group of stars among 
which the new moon was first seen was accurately noted, so as to be rec- 
ognized at the following new moon, and doubtless our primitive astronomer 
hoped to find that in this same group the silver crescent, when it should 
next appear, would be found. But in this he was disappointed ; for when 
the moon became first faintly visible in the western sky, the group of stars 
which had ushered her in before, had disappeared below the horizon, and 
a new group had taken its place ; and thus it was discovered that each 
successive new moon fell farther and farther backward among the stars. By 
counting the days from new moon to new moon, and those which elapsed 
while the moon was passing round the heavens from a certain fixed star to 
this same star again, it was found, that these two periods were different ; the 
revolution from new to new occupying 29h days, while the sidereal revolu- 
tion, from star to star, required 21h days. 

This backward motion of the moon among the stars, must have per- 
plexed the early astronomers ; and for a long while it was utterly impos- 
sible to decide whether the motion was real or only apparent — analogy 
would lead to the conclusion that all motion must be in the same di- 
rection, and as the heavens revolved from east to west, it seemed impos- 
sible that the moon, which manifestly participated in this general move- 
ment, should have another and a different motion, from west to east. 
There was one solution of this mystery, and I have no doubt it was for a 
long while accepted and believed. It was this. By giving to the moon 
a slower motion from east to west, than the general motion of the heavens, 
she would appear to lag behind the stars, which would by their swifter ve- 
locity pass by her, and thus occasion in her the observed apparent motion, 
from west to east. We shall see presently how this error was detected. 

The long and accurate vigils of the moon, and the necessity of recogniz- 
ing her place, by the clusters of groups of stars among which she was 
nightly found, had already familiarized the eye with those along her 
track, and even thus early the heavens began to be divided into constella- 
tions. The eye was not long in detecting the singular fact, that this 
stream of constellations, lying along the moon's path, was constantly 
flowing to the west, and one group after another apparently dropping 
into the sun, or at least becoming invisible in consequence of their prox- 
imity to this brilliant orb. A closer examination revealed the fact, that 
the aspect of the whole heavens was changing from month to month. 
Constellations which had been conspicuous in the west, and whose brighter 
stars were the first to appear as the twilight faded, were found to sink 
lower and lower towards the horizon, till they were no longer seen ; while 
new groups were constantly appearing in the east. 

These wonderful changes, so strange and inexplicable, must have long 



28 STRUCTURE OF THE UNIVERSE, 

perplexed the early student of the heavens. Hitherto the stars along the 
moon's route, had engaged special attention ; but at length certain bright and 
conspicuous constellations, towards the north, arrested the eye : and these 
were watched to see whether they would disappear. — Some were found to 
dip below the western horizon, soon to re-appear in the east ; while others 
revolving with the general heavens, rose high above the horizon, swept 
steadily round, sunk far down, but never disappeared from the sight. This 
remarkable discovery soon led to another equally important. In watching 
the stars in the north through an entire night, they all seemed to describe 
circles ; having a common center, these circles grew smaller and smaller 
as the stars approached nearer to the center of revolution, until finally 
one bright star was found, whose position was ever fixed — Alone unchanged 
while all else was slowly moving. The discovery of this remarkable star, 
must have been hailed with uncommon delight by the primitive observer of 
the heavens. If his deep devotion to the study of the skies, had created 
surprise among his rude countrymen, when he came to point them to this 
never changing light hung up in the heavens, and explained its uses in 
guiding their wanderings on the earth, their surprise must have given 
place to admiration. Here was the first valuable gift of primitive as- 
tronomical science to man. 

But to the astronomer this discovery opened up a new field of investiga- 
tion, and light began to dawn on some of the most mysterious questions 
which had long perplexed him. He had watched the constellations near 
the moon's track slowly disappear in the effulgence of the sun, and when 
they were next seen, it was in the east, in the early dawn, apparently 
emerging from the solar beams, having actually passed by the sun. Watch- 
ing and reflecting, steadily pursuing the march of the northern constella- 
tions, which never entirely disappeared, and noting the relative positions 
of these, and those falling into the sun, it was at last discovered that 
the entire starry heavens was slowly moving forward to meet and 
pass by the sun, or else the sun itself was actually moving backward 
among the stars. This apparent motion had already been detected in the 
moon, and now came the reward of long and diligent perseverance. The 
grand discovery was made, that both the sun and moon were moving 
among the fixed stars, not apparently, but absolutely. The previously 
received explanation of the moon's motion, could no longer be sustained ; 
for the starry heavens could not at the same time so move as to pass by 
the moon in one month, and to past by the sun in a period twelve times 
as great. A train of the most important conclusions flowed at once from 
this great discovery. — The starry heavens passed beneath and around the 
earth, — the sun and moon were wandering in the same direction, but with 
different velocities among the stars, — the constellations actually filled the 
entire heavens above the earth and beneath the earth, — the stars were in- 
yisible in the day time, not because they did not exist, but because their 



THE DISCOVERIES OF THE PRIMITIVE AGES. 29 

feeble light was lost in the superior brilliancy of the sun. The heavens 
were spherical, and encompassed like a shell the entire earth, and hence it 
was conceived that the earth itself was also a globe, occupying the center 
of the starry sphere. 

It is impossible for us, familiar as we are at this day with these im- 
portant truths, to appreciate the rare merit of him who by the power of 
his genius, first rose to their knowledge and revealed them to an as- 
toished world. We delight to honor the names of Kepler, of Galileo, of 
Newton ; but here are discoveries so far back in the dim past, that all 
trace of their origin is lost, which vie in interest and importance with the 
proudest achievements of any age. 

With a knowledge of the sphericity of the heavens, the revolution of 
the sun and moon, the constellations of the celestial sphere, the axis of 
its diurnal revolution, astronomy began to be a science, and its future 
progress was destined to be rapid and brilliant. A line drawn from the 
earth's center to the north star formed the axis of the heavens, and day and 
night around this axis all the celestial host were noiselessly pursuing their 
never ending journeys. — Thus far, the only moving bodies known, were 
the sun and moon. These large and brilliant bodies, by their magnitude 
and splendor, stood out conspicuously, from among the multitude of stars, 
leaving these minute but beautiful points of light, in one great class, un- 
changeable among themselves, fixed in their grouping and configurations, 
furnishing admirable points of reference, in watching and tracing out the 
wanderings of the sun and moon. 

To follow the moon as she pursued her journey among the stars was 
not difficult ; but to trace the sun in his slower and more majestic motion, 
and to mark accurately his track, from star to star, as he heaved upward 
to meet the coming constellations, was not so readily accomplished. 
Night after night, as he sunk below the horizon, the attentive watcher 
marked the bright stars near the point of setting which first appeared in 
the evening twilight.- — These gradually sunk towards the sun on suc- 
cessive nights, and thus was he traced from constellation to constellation, 
until the entire circuit of the heavens was performed, and he was once 
more attended by the same bright stars, that had watched long before, his 
sinking in the west. Here was revealed the measure of the Year. The 
earth had been verdant with the beauties of spring, — glowing with the 
maturity of summer, — rich in the fruits of autumn, — and locked in the 
icy chains of winter, while the sun had circled round the heavens. His 
entrance into certain constellations marked the coming seasons, and man 
was beginning to couple his cycle of pursuits on earth with the revolu- 
tions of the celestial orbs. 

While intently engaged in watching the sun as it slowly heaved up to 
meet the constellations, some ardent devotee to this infant science, at 
length marked in the early twilight a certain brilliant star closely attend- 



80 STRUCTURE OF THE UNIVERSE. 

ant upon the sun. The relative position of these two objects was noted, 
for a few consecutive nights, when with a degree of astonishment of 
which we can form no conception, he discovered that this brilliant star 
was rapidly approaching the sun, and actually changing its place among 
the neighboring stars, — night after night he gazes on this unprecedented 
phenomenon, a moving star! and on each successive night he finds the 
wanderer coming nearer and nearer to the sun. At last it disappears from 
sight, plunged in the beams of the upheaving sun. What had become of 
this strange wanderer ? was it lost forever ? were questions which were 
easier asked than answered. — But patient watching had revealed the fact, 
that when a group of stars, absorbed into the sun's rays, disappeared in 
the west, they were next seen in the eastern sky, slowly emerging from 
his morning beams. Might it not be possible, that this wandering star 
would pass by the sun and re-appear in the east ? With how much anx- 
iety must this primitive discoverer have watched in the morning twi- 
light ? Day after day he sought his solitary post, and marked the rising 
stars, slowly lifting themselves above the eastern horizon. The gray 
dawn came, and the sun shot forth a flood of light, the stars faded and 
disappeared, and the watcher gives over, till the coming morning. But 
his hopes are crowned at last. Just before the sun breaks above the 
horizon, in the rosy east, refulgent with the coming day, he descries the 
pure white silver ray of his long lost wanderer. It has passed the sun, — 
it rises in the east, — the first planet is discovered ! 

With how much anxiety and interest did the delighted discoverer trace 
the movements of his wandering star. Here was a new theme for 
thought, for observation, for investigation ; would this first planet sweep 
round the heavens, as did the sun and moon ? would it always move in 
the same direction ? would its path lie among those groups of stars 
among which the sun and moon held their course? Encouraged by 
past success, he rejoicingly enters on the investigations of these ques- 
tions. For some time the planet pursues its journey from the sun, 
leaving it farther and farther behind. But directly it slackens its 
pace, — it actually stops in its career, and the astonished observer 
perhaps thinks that his wandering star had again become fixed. Not 
so, — a few days of watching dispels this idea. Slowly at first and 
soon more swiftly, the planet seeks again the sun, moving backwards 
on its former path, until finally its light is but just visible in the east at 
early dawn. Again it is lost in the sun's beams for a time, and contrary 
to all preceding analogy, when next seen, its silver ray comes out pure 
and bright, just above the setting sun. It now recedes from the sun, on 
each successive evening increasing its distance, till it again reaches a point 
never to be passed — here it stops — is stationary for a day or two, and 
then again sinks downward to meet the sun. How wonderful and inex- 
plicable the movements of this wandering star must have appeared in the 



TEE DISCOVERIES OF THE PRIMITIVE AGES. 31 

early ages ! oscillating backward and forward, never passing its prescribed 
limits, and ever closely attendant upon the sun. Where the sun sunk 
to repose, there did the faithful planet sink, and where the sun rose, at 
the same point did the wandering star make its appearance. The number 
of days was accurately noted, from the stationary point in the east above 
the sun, to the stationary point in the west above the sun, and thus the 
period, 584 days from station to station, became known. 

The discovery of one planet, led the way to the rapid discovery 
of several others. If we may judge of their order by their brilliancy, 
Jupiter was the second wanderer revealed among the stars. Then 
followed Mars, and Saturn, and after a long interval Mercury was 
detected, hovering near the sun, and imitating the curious motions of 
Venus. 

Here the progress of planetary discovery was suddenly arrested, keen 
as was the vision of the old astronomer, long and patient as was his 
scrutiny, no depth of penetration of unaided vision could stretch beyond 
the mighty orbit of Saturn, and the search was given over. — A close ex- 
amination of the planets revealed many important facts. Three of them, 
Mars, Jupiter, and Saturn, were found to perform the circuit of the 
heavens, like the sun and moon, and in the same direction ; with this 
remarkable difference, that while the sun and moon, moved steadily and 
uniformly in the same direction, the planets occasionally slackened their 
pace, would then stop, move backwards on their track, stop again, and 
finally resume their onward motion. Their periods of revolution were 
discovered by marking the time which elapsed, after setting out from 
some brilliant and well known fixed star, until they should perform the 
entire circuit of the heavens and once more return to the same star. The 
times of revolution were found to differ widely from each other ; Mars 
requiring about 687 days, Jupiter 4,332 days, and Saturn 10,759 days, or 
nearly thirty of our years. 

The planets all pursued their journeys in the heavens, among the same 
constellations which marked the paths of the sun and moon, and hence 
these groups of stars concentrated the greatest amount of attention among 
the early astronomers, and became distinguished from all the others. 

Whatever light may be shed upon antiquity by deciphering the 
hieroglyphic memorials of the past there is no hope of ever going far 
enough back, to reach even the nation, to which we are indebted for the 
first rudiments of the science of the stars. 

Thus far in the prosecution of the study of the heavens, the eye and the 
intellect had accomplished the entire work. Rapidly as we have sketched 
the progress of early discovery, and short as may have been the period 
in which it was accomplished, no one can fail to perceive, how vast is the 
difference between the light that thus early broke in upon the mind, herald 
ing the coming of a brighter day, and the deep and universal darkness 



82 STRUCTURE OF THE UNIVERSE. 

which had covered the world, before the dawn of science. Encour- 
aged by the success which had thus far rewarded patient toil, the 
mind of man pushes on its investigations deeper and deeper into the 
domain of the mysterious and unknown. 

In watching the annual revolution of the sun among the fixed stars, 
one remarkable peculiarity had long been recognized. While the interval 
of time, from the rising to the setting of the stars, was ever the same at all 
seasons of the year, the interval from the rising to the setting of the sun 
was perpetually changing, passing through, a cycle which required exactly 
one year for its completion. It became manifest that the sun did not 
prosecute its annual journey among the stars, in a circle parallel with 
those described by the stars, in their diurnal revolution. His path was 
oblique to those circles, and while he participated in their diurnal motion, 
he was sweeping by his annual revolution round the heavens, and was at 
the same time, by another most extraordinary movement, carried towards 
the north to a certain distance, then stopping, commenced a return 
towards the south, — reached his southern limit, — again changed his direc- 
tion, and thus oscillated from one side to the other of his mean position. 

These wonderful changes became the objects of earnest investigation. 
In what curve did the sun travel among the stars ? All diurnal motion 
was performed in a circle, the first discovered, the simplest and the most 
beautiful of curves : and in this curve, analogy taught the early astron- 
omers, that all celestial movements must be performed. It became 
therefore, a matter of deep interest, to trace the sun's path accurately 
among the stars, to mark his track, and to see whether it would not 
prove to be a circle. To accomplish this, more accurate means must be 
adopted, than the mere watching of the stars which attended the rising or 
setting sun. The increase and decrease of the shadow of some high 
pointed rock, to whose refreshing shade the shepherd astronomer had 
repaired in the heat of noon, and beneath which he had long pondered 
this important problem, first suggested the means of its resolution. — As 
the summer came on he remarked that the length of the noon shadow of 
his rock, perpetually decreased from day to day. As the sun became 
more nearly vertical at noon, the shadow gave him less and less shelter. 
Watching these noon shadows, from day to day, he found them 
proportioned to the sun's northern or southern motion, and finally the 
thought entered his mind, that these shadows would mark with certainty 
the limits of the sun's motion north and south, — the character of .his 
orbit or route among the stars, — the changes and duration of the seasons, 
and the actual length of the year, which thus far had been but roughly- 
determined. To accomplish the observations more accurately, an area on 
the ground was smoothed and leveled, and in its centre a vertical pole 
was erected some ten or fifteen feet in length, whose sharp vertex cast a 
well defined shadow. And here we have the first astronomical instru- 



THE DISCOVERIES OF THE PRIMITIVE AGES. £8 

ment, the gnomon, ever devised by the ingenuity of man. Simple as it 
is, by its aid the most valuable results were obtained. 

The great point was to mark with accuracy the length of the noon-day 
shadow, from month to month, throughout the entire year. Four remark- 
able points in the sun's annual track, were very soon detected and 
marked. One of these occurred in the summer, and was that point 
occupied by the sun on the day of the shortest noon shadow. Here the 
sun had reached his greatest northern point, and for a few days the noon 
shadow, cast by the gnomon appeared to remain the same, and the sun 
stood still. The noon shadows now increased slowly, for six months, as 
the sun moved south, till a second point was noted, when the noon 
shadow had reached its greatest length. Again it became stationary, 
and again the sun paused and stood still, before commencing his return 
towards the north. These points were called the summer and winter 
solstices, and occurred at intervals of half a year. At the summer solstice, 
the longest day occurred, while at the winter solstice, the shortest day 
was always observed. These extreme differences between the length of 
the day and night, occasioned' the determination of the other two points. 
From the winter solstice, the noon shadows decreased as the length of 
the day increased, until finally the day and night were remarked to be of 
equal length, and the distance to which the shadow of the gnomon was 
thrown on that day, was accurately fixed. If on this day the diurnal 
circle described by the sun, could have been marked in the heavens by a 
circle of light, sweeping from the east to the west, so that the eye might 
rest upon and retain it, and if at the same time the sun's annual path, 
among the fixed stars could have been equally exhibited in the heavens 
by a circle of light, these two circles would have been seen to cross each 
other, and at their point of crossing, the sun would have been found. 
The diurnal circle was called the equator, the sun's path the ecliptic, and 
the point of intersection was called appropriately, the equinox. — As the 
sun crossed the equator in the spring and autumn, these points received 
the names of the vernal and autumnal equinoxes , and were marked with 
all the precision which the rude means then in use rendered practicable. 

The bright circle already imagined in the heavens to represent the sun's 
annual track among the stars, passed obliquely across the equator, and 
the amount by which these circles w ere inclined to each other was actual- 
ly measured in these early ages, with no mean precision by the noon shad- 
ows of the gnomon. The ray casting the shortest noon shadow, was 
inclined to the ray forming the longest noon shadows, under an angle 
precisely double of the inclination of the ecliptic or sun's path to the 
equator, and the inclination of these two rays marked exactly the annual 
motion of the sun from south to north, or from north to south. A close 
examination of the order of increase and decrease in the length of the noon 
shadows cast by the gnomon, demonstrated the important truth already 



34 STBUCTURE OF THE UNIVERSE. 

suspected, that the sun's path was actually a circle, but inclined, as lias 
already been shown, to the diurnal circles of the stars and to the equa- 
tor. 

By counting the days which elapsed from the summer solstice to the 
summer solstice again, a knowledge of the length of the year, or period 
of the sun's revolution, was obtained. But here again a discovery was 
made which produced an embarrassment to the early astronomer, which 
all their perseverance and research never succeeded in removing, 

In these primitive ages the heavenly bodies were regarded with feel- 
ings little less than the reverence we now bestow on the Supreme Creator. 
The sun especially, as the Lord of life and light, was regarded with feel- 
ings nearly approaching to adoration, even by the astronomers them- 
selves. The idea early became fixed, that the chief of the celestial bodies 
must move with a uniform velocity in a circular orbit, never increasing or 
decreasing. Change being inconsistent with the supreme and dignified 
station which was assigned to him — what then must have been the aston- 
ishment of the primitive astronomers, who in counting the days from the 
summer to the winter solstice, and from the winter round to the summer 
solstice, these intervals were found to be unequal. — This almost incredi- 
ble result was confirmed, by remarking that the shortest spaces from equi- 
nox to solstice, dividing the sun's annual route, into four equal portions, 
were passed over in unequal times. These results could not be doubted, 
for each observation, from year to year, confirmed them. They were 
received and recorded, but the problem was handed down to succeeding 
generations for solution. 

In consequence of the oblique direction of the ecliptic or sun's track, 
it was found difficult to retain its position in the mind. To assist in the 
recurrence to this important circle, a brazen circle was at length devised, 
and fastened permanently to another brazen circle of equal size, under an 
angle, exactly equal to the inclination of the equator to the ecliptic. Cir- 
cles, perpendicular to the equator, and passing through the solstices and 
equinoxes, completed the second astronomical instrument, the sphere. 
Having constructed this simple piece of machinery, it was mounted on an 
axis passing through its centre, and perpendicular to its equator, so as to 
revolve, as did the heavens, whose motions it was intended to represent. 
Having so placed the axis of rotation, that its prolongation would pass 
through the north star, this rude sphere came to play a most important 
part in the future investigations of the heavens. Its brazen equator an<? 
ecliptic were each divided into a certain number of equal parts, by refer- 
ence to which the motion of the heavenly bodies might be followed, with 
far greater precision, than had ever been previously obtained. 

Armed with a new and more perfect instrument, the astronomer re- 
sumes his great investigation. Finding it now possible, to mark out the 
sun's path in the heavens, with certainty, by means of his brazen ecliptic, 



THE DISCOVERIES OF THE PRIMITIVE AGES. 35 

he discovers that the moon and planets in each revolution pass across the 
sun's track, and spend nearly an equal amount of time on the north and 
south sides of the ecliptic. This discovery led to a more accurate deter- 
mination of the periods of revolution of the planets. The interval was 
noted from one passage across the ecliptic to the next on the same side, 
and these intervals marked with accuracy the planetary periods. It now 
became possible to fix, with greater certainty, the relative positions of the 
sun and moon, and problems were once more resumed which had thus far 
baffled every effort of human genius. The phases of the moon, the very 
first point of investigation, had never yet yielded up its hidden cause, and 
those terrific phenomena, solar and lunar eclipses, which had long covered 
the earth with terror and dismay, were wrapped in mystery, and their 
explanation had resisted the sagacity of the most powerful and gifted 
intellects. 

No one has ever witnessed the going out of the sun in dim eclipse, even 
now when its most minute, phenomena are predicted with rigorous exact- 
itude, without a feeling of involuntary dismay. What then must have 
been the effect upon the human mind in those ages of the world, when 
the cause was unknown and when these terrific exhibitions burst on 
earth's inhabitants unheralded and unannounced? Here then was an 
investigation, not prompted by curiosity alone, but involving the peace 
and security of man in all coming ages. We cannot doubt that the 
causes of the solar eclipse were first detected. It was observed, that no 
eclipse of the sun ever occurred, when the moon was visible. Even during 
a solar eclipse, when the sun's light had entirely faded away, and the stars 
and planets stole gently upon the sight in the sombre and unnatural 
twilight, the moon was sought for in vain ; she was never to be seen. 
This fact excited curiosity and gave rise to a careful and critical exami- 
nation of the place in which the moon should be found, immediately after 
a solar eclipse ; and it was soon discovered that on the night following 
the day of eclipse, the moon was seen in her crescent shape very near to 
the sun and but a short distance from the sun's path. By remarking the 
moon's places, next before a solar eclipse and that immediately following, 
it was seen that at the time of the occurrence of the eclipse, the moon was 
actually passing from the west to the east side of the sun's place, and 
finally a little calculation showed that a coincidence of the sun and moon 
in the heavens took place at the precise time at which the sun had been 
eclipsed. The conclusion was irresistible, and the great fact was an 
nounced to the world, that the sun's light was hidden by the interposition 
of the dark body of the moon. 

Having reached this important result with entire certainty, the expla- 
nation of the moon's phases followed in rapid succession. For it now 
became manifest, that the moon shone with borrowed light, and that her 
brilliancy came from the reflected beams of the sun. This was readily 



36 STRUCTURE OF THE UNIVERSE. 

demonstrated by the following facts. When the moon was so situated 
that the side next to the sun, (the illuminated one), was turned from the 
eye of the observer, (as was the case in a solar eclipse), then the moon's 
surface next to the observer, was always found to be entirely black. Pur- 
suing her journey from this critical point, the moon was next seen near 
the sun, in the evening twilight, as a slender thread of light, a very small 
portion of her illuminated surface being now visible. Day after day this 
visible portion increases, until finally the moon rises as the sun sets, full 
orbed and round, being directly opposite the sun, and turning her entire 
illuminated surface towards the eye of the observer. By like degrees she 
loses her light as she approaches, and finally becomes invisible as she 
passes by the sun. From this examination it became evident that the moon 
was a globular body, non-luminous, and revolving in an orbit, compre- 
hended entirely within that described by the sun, and consequently, nearer 
to the earth than the sun. Having ascertained this fact, it was concluded 
that among all the moving heavenly bodies, the periods of revolution 
indicated their relative distances from the earth. Hence Mars was re- 
garded as more distant than the sun, Jupiter more remote than Mars, and 
Saturn the most distant, as it was the slowest moving of all the planets. 
After reaching to a knowledge of the causes producing the eclipse of 
the sun and the phases of the moon, it remained yet to resolve the mystery 
of the lunar eclipse. It was far more difficult to render a satisfactory ac- 
count of this phenomenon than either of the preceding. The light of the 
moon was not intercepted by the interposition of any opaque body, between 
it and the eye of the observer. No such body existed, and long and per- 
plexing was the effort to explain this wonderful phenomenon. Finally it 
was observed that all opaque bodies cast shadows, in directions opposite 
to the source of light. Was it not possible that the light of the sun, 
falling upon the earth, might be intercepted by the earth, and thus pro- 
duce a shadow which might even reach as far as the moon? So soon as 
this conjecture was made, a series of examinations were commenced to 
confirm or destroy the theory. It was at once seen that in case the con- 
jecture was true, no lunar eclipse could occur except when the sun, earth 
and moon, were situated in the same straight line ; a position which could 
never occur, except at the full or new of the moon. It was soon discovered 
that, it was only at the full, that lunar eclipses took place, thus con- 
firming the truth of the theorj*, and fixing it beyond a doubt that the 
shadow of the earth falling on the moon, was the cause of her eclipse. 
The moon had already been shown to be non-luminous, and the moment 
the interposition of the earth, between it and its source of light, the sun, 
cut off its light, it ceased to be visible, and passed through an eclipse. 
The sphericity of the earth, which had been analogically inferred from 
that of the heavens was now made absolutely certain — for it was remark- 
ed, that as the moon entered the earth's shadow, that_ the , track of this 



THE DISCOVERIES OF THE PRIMITIVE AGES. 37 

dark shadow across the bright surface of the moon was always circular, 
which was quite impossible, for every position except the earth, which 
cast this circular shadow, should be of a globular form. 

Having now attained to a clear and satisfactory explanation of the two 
grand phenomena, solar and lunar eclipses, the question naturally arose, 
why was not the sun eclipsed in each revolution of the moon ; and 
how happened it that the moon in the full, did not always pass through 
the earth's shadow ? An examination of the moon's path among the 
fixed stars gave to these questions a clear and positive answer. It 
was found that the sun and moon did not perform their revolutions 
in the same plane. The moon's route among the stars crossed the 
sun's route under a certain angle, and it thus frequently happened, 
that at the new and full, the moon occupied some portion of her orbit 
too remote from that of the sun to render either a lunar or solar eclipse 
possible. 

Rapidly have we traced the career of discovery. The toil and watch- 
ing of centuries have been condensed into a few moments of time, and 
questions requiring ages for their solution have been asked, only to be 
be answered. In connection with the investigations just developed, and 
as a consequence of their successful prosecution, the query arose whether 
in case science had reached to a true exposition of the causes producing 
the eclipse of the sun, was it not possible to stretch forward in time, and 
anticipate and predict the coming of these dread phenomena ? 

To those who have given but little attention to the subject, even in 
our own day, with all the aids of modern science, the prediction of an 
eclipse, seems sufficiently mysterious and unintelligible. How then it 
was possible, thousands of years ago, to accomplish the same great object, 
without any just views of the structure of the system, seems utterly in- 
credible. Follow me, then, while I attempt to reveal the train of reason- 
ing which led to the prediction of the first eclipse of the sun, the most 
daring prophecy ever made by human genius. Follow in imagination, 
this bold interrogator of the skies to his solitary mountain summit — with- 
drawn from the world — surrounded by his mysterious circles, there to 
watch and ponder through the long nights of many — many years. But 
hope cheers him on, and smooths his rugged pathway. Dark and deep as 
is the problem, he sternly grapples with it, and resolves never to give 
over till victory crowns his efforts. 

He has already remarked, that the moon's track in the heavens crossed 
the sun's, and that this point of crossing was in some way intimately con- 
nected with the coming of the dread eclipse. He determines to watch 
and learn whether the point of crossing was fixed, or whether the moon 
in each successive revolution, crossed the sun's path at a different point. 
If the sun in its annual revolution could leave behind him a track of fir© 
marking his journey among the stars, it is found that this same track was 



$g STRUCTURE OF THE UNIVERSE. 

followed from year to year, and from century to century with undeviating 
precision. But it was soon discovered, that it was far different with, the 
moon. In case she too could leave behind her a silver thread of light 
sweeping round the heavens, in completing one revolution, this thread 
would not join, but would wind around among the stars in each revolu- 
tion, crossing the sun's fiery track at a point west of the pre/ious cross- 
ing. These points of crossing were called the moon's nodes. At each 
revolution the node occurred further west, until after a cycle of about 
nineteen years, it had circulated in the same direction entirely round the 
ecliptic. Long and patiently did the astronomer watch and wait, each 
eclipse is duly observed, and its attendant circumstances are recorded, 
when, at last, the darkness begins to give way and a ray of light breaks 
in upon his mind. He finds that no eclipse of the sun ever occurs unless the 
new moon is in the act of crossing the suns track. Here was a grand discov- 
ery. — He holds the key which he believes will unlock the dread mystery 
and now, with redoubled energy, he resolves to thrust it into the wards 
and drive back the bolts. 

To predict an eclipse of the sun, he must sweep forward, from new 
moon to new moon, until he finds some new moon which should occur, 
while the moon was in the act of crossing from one side to the other of the 
sun's track. — This certainly was possible. He knew the exact period from 
new moon to new moon, aud from one crossing of the ecliptic to another, 
with eager eye he seizes the moon's place in the heavens, and her age, and 
rapidly computes where she will be at her next change. He finds the new 
moon occurring far from the sun's track ; he runs round another revolu- 
tion ; the place of the new moon falls closer to the sun's path, and the 
next yet closer, until reaching forward with piercing intellectual vigor, he 
at last, finds a new moon which occurs precisely at the computed time of 
her passage across the sun's track. Here he makes his stand, and on the 
day of the occurrence of that new moon, he announces to the startled in- 
habitants of the world, that the sun shall expire in dark eclipse — Bold pre- 
diction ! — Mysterious prophet ! with what scorn must the unthinking world 
have received this solemn declaration. How slowly do the moons roll away, 
and with what intense anxiety does the stern philosopher await the com- 
ing of that day which should crown him with victory, or dash him to the 
ground in ruin and disgrace. Time to him moves on leaden wings ; day 
after day, and at last hour after hour, roll heavily away. The last night is 
gone — the moon has disappeared from his eagle gaze in her approach to 
the sun, and the dawn of the eventful day breaks in beauty on a slumbering 
world. 

This daring man, stern in his faith, climbs alone to his rocky home, 
and greets the sun as he rises and mounts the heavens, scattering brightness 
and glory in his path. Beneath him is spread out the populous city, 
already teeming with life and activity. The busy morning hum rises on 



TEE DISCOVERIES OF THE PRIMITIVE AGES. 39 

the still air and reaches the watching place of the solitary astronomer. 
The thousands below him, unconscious of his intense anxiety, buoyant 
with life, joyously pursue their rounds of business, their cycles of amuse- 
ment. The sun slowly climbs the heavens, round and bright and 
full orbed. The lone tenant of the mountain-top almost begins to waver 
in the sternness of his faith, as the morning hours roll away. But the 
time of his triumph, long delayed, at length begin to dawns ; a pale and 
sickly hue creeps over the face of nature. The sun has reached his highest 
point, but his splendor is dimmed, his light is feeble. At last it comes ! 
— Blackness is eating away his round disk, — onward with slow but steady 
pace, the dark veil moves, blacker than a thousand nights- — the gloom 
deepens, — the ghastly hue of death covers the universe, — the last ray is 
gone, and horror reigns. A wail of terror fills the murky air, — the clangor 
of brazen trumpets resounds, — an agony of despair dashes the stricken 
millions to the ground, while that lone man, erect on his rocky summit, 
with arms outstretched to heaven, pours forth the grateful gushings of his 
heart to God, who had crowned his efforts with triumphant victory. Search 
the records of our race, and point me, if you can, to a scene more grand, 
more beautiful. It is to me the proudest victory that genius ever won. It 
was the conquering of nature, of ignorance, of superstition, of terror, all at a 
single blow, and that blow struck by a single arm. — And now do you 
demand the name of this wonderful man ! Alas ! what a lesson of the 
instability of earthly fame are we taught in this simple recital. — He who 
had raised himself immeasurably above his race, — who must have been re- 
garded by his fellows as little less than a god, who had inscribed his fame 
on the very heavens, and had written it in the sun, with a " pen of iron, 
and the point of a diamond," even this one has perished from the earth — 
name, age, country, are all swept into oblivion, but his proud achievement 
stands. The monument reared to his honor stands, and although the touch 
of time has effaced the lettering of his name, it is powerless, and cannot 
destroy the fruits of his victory. 

A thousand years roll by : the astronomer stands on the watch tower of 
old Babylon, and writes for posterity the records of an eclipse ; this record 
escapes destruction, and is safely wafted down the stream of time. A 
thousand years roll away: the old astronomer, surrounded by the fierce, 
but wondering Arab again writes, and marks the day which witnesses 
the sun's decay. A thousand years rolls heavily away: once more the 
astronomer writes from amidst the gay throng that crowds the brightest 
capital of Europe. Record is compared with record, date with date, revolu- 
tion with revolution, the past and present are linked together, — another 
struggle commences, and another victory is won. Little did the Babylonian 
dream that he was observing for one who after the lapse of 3000 years, 
should rest upon records, the successful resolution of one of nature's 
darkest mysteries. 



4® 8RTUCTUBE OF THE UNIVERSE. 

"W© have now reached the boundary where the stream of discovery, 
which we have been tracing through the clouds and mists of antiquity, 
begins to emerge into the twilight of tradition, soon to flow on in the clear 
light of a history that shall never die. Henceforth our task will be more 
pleasing, because more certain ; and we invite you to follow us as we 
attempt to exhibit the coming struggles and future triumphs of the student 
of the skies. 



LMJFUH& in. 

THEOKIBS FOR MB EXPLANATION OF THE MOTIONS OF THE 

HEAVENLY BODIES. 

If in tracing the career of astronomy in the primitive ages of the 
world, we have been left to pnrsne our way dimly, through cloud and 
darkness, — if regrets rise up, that time has swept into oblivion the names 
and country of the early discoverers, in one reflection there is some com- 
pensation — while the bright and enduring truths which they wrested 
from nature have descended to us, their errors, whatever they may have 
been, are forever buried with their names and their persons. We are 
almost led to believe that those errors were few and transient, and that 
the mind, as yet undazzled by its triumphs, questioned nature, with that 
humility and. quiet perseverance, which could bring no response but 
truth. 

In pursuing the consequences flowing from the prediction of an eclipse, 
several remarkable results were reached, which we proceed to unfold. It 
will be recollected, that to produce either solar or lunar eclipses, the new 
or full moon must be in the act of crossing the sun's annual track. This 
point of crossing, called the moon's node, became therefore an object of the 
deepest interest. Long and careful scrutiny revealed the fact of its 
movement around the ecliptic, in a period of eighteen years and eleven 
days, during which time there occur 223 new moons, or 223 full moons. 
If then, a new moon falls on the sun's track to produce a solar eclipse to- 
day, at the expiration of 223 lunations, again will the new moon fall on 
the ecliptic, and an eclipse will surely take place. Suppose then that all 
the eclipses, which occur within this remarkable period of 223 lunations, 
are carefully observed, and the days on which they fall recorded, on each 
and every one of these days, during the next period of 223 lunations, 
eclipses may be expected, and their coming foretold. 

This wonderful period of eighteen years and eleven days, or 223 luna- 
tions, was known to the Chaldeans, and by its use eclipses were predicted, 
more than 3000 years ago. It is likewise found among the Hindus, the 
Chinese, and the Egyptians, nations widely separated on the earth's 
surface, and suggesting the idea that it had its origin among a people 
even anterior to the Chaldeans. It is now known by the name of the 
Zaros, or Chaldean period. 

Let it not be supposed that the application of the Zaros to the predic- 
tion of eclipses, can in any way supersede modern methods. — While antiq- 



42 STRUCTURE OF TH.fi UNIVERSE, 

uity contented itself with announcing the ~day~ 6n~which the dark body 
of the moon should hide the sun, modern science points to the exact 
second on the dial, which shall mark the first delicate contact of the 
moon's dark edge with the brilliant disk of the sun. 

It would be a matter of great interest to fix the epoch of primitive 
discovery. Though this is impossible, its high antiquity is attested by a 
few facts, to which we will briefly advert. We find among all the ancient 
nations, Chaldeans, Persians, Hindus, Chinese, and Egyptians, that the 
seven days of the week were in universal use, and what was far more 
remarkable, each of these nations named the days of the week after the 
seven planets, numbering the sun and moon among the planets. It is 
moreover found, that the order of naming is not that of the distance, 
velocity or brilliancy of the planets, and neither does the first day of the 
week coincide among the different nations ; but the order once commenced 
is invariably preserved by all. If we compute the probability of such a 
coincidence resulting by accident, we shall find the chances millions to 
one against it. We are therefore forced to the conclusion, that the planets 
were discovered, and the seven days of the week devised and named, by 
some primitive nation, from whom the tradition descended imperfectly, 
to succeeding generations. 

A remarkable discovery, made in the remote ages of the world, throws 
some farther light on the era of the primitive astronomical researches. — 
The release of the earth from the icy fetters of winter, the return of 
spring, and the revivification of nature, is a period hailed with uncommon 
delight, in all ages of the world. To be able to anticipate its coming, 
from some astronomical phenomenon, was an object of earnest investi- 
gation by the ancients. 

It was found that the sun's entrance into the equinox, reducing to 
equality the length of the day and night, always heralded the coming of 
the spring. Hence to mark the equinoctial point among the fixed stars, 
and to note the place of some brilliant star whose appearance in the early 
morning dawn, would announce the sun's approach to the equator, was 
early accomplished with all possible accuracy. This star once selected, 
it was believed that it would remain forever in its place. 

The sun's path among the fixed stars had been watched with success, 
and it seemed to remain absolutely unchanged, and hence the points in 
which it crossed the equator, for a long while were looked upon as fixed 
and immovable. And indeed centuries must pass away before any change 
could become sensible to the naked eye and its rude instrumental aux- 
iliaries. But a time arrives at last when the bright star which for more 
than five hundred years had, with its morning ray announced the season 
of flowers, is lost. It has failed to give its warning — spring has come, 
the forests bud, the flowers bloom, but the star which once gave promise, 
and whose ray had been hailed with so much delight by many generations, 



MOTIONS OF THE EEAVEFLY BODIES. 4S 

ig no longer found. The hoary patriarch recalls the long experience of a 
hundred years, and now perceives, that each succeeding spring had 
followed more and more rapidly after the appearance of the sentinel star. 
Each year the interval from the first appearance of the star in the early 
dawn, up to the equality of day and night, had grown less and less, and 
now the equinox came, but the star remained invisible, and did not 
emerge from the sun's beams until the equinox had passed. 

Long and deeply were these facts pondered and weighed. — At length 
truth dawned, and the discovery broke upon the unwilling mind, that the 
sun's path among the fixed stars was actually changing, and that his point 
of crossing the equator was slowly moving backwards towards the west 
and leaving the stars behind. The same motion, only greatly more rapid, 
had been recognized in the shifting of the moon's node and in the rapid 
motion of the points at which her track crossed the equator. The retro- 
grade motion of the equinoctial points, caused the sun to reach these points 
earlier than it would have done had they remained fixed, and hence arose 
the precession of the equinoxes. 

This discovery justly ranks among the most important achieved by an- 
tiquity. Its explanation was infinitely above the reach of human effort at 
that early day : but to have detected the fact, and to have marked a motion 
so slow and shrouded, gives evidence of a closeness of observation worthy 
of the highest admiration. It will be seen hereafter, that the human mind 
has reached to a full knowledge of the causes producing the retrograde 
movement of the equinoxes among the stars. Its rate of motion has been 
determined, and its vast period of nearly twenty-six thousand years has 
been fixed. Once revealed, the slow movement of the equinox, makes it 
a fitting hour hand, on the dial of the heavens, with which to measure the 
revolutions of ages. As the sun's path has been divided into twelve con- 
stellations, each filling the twelfth part of the entire circuit of the heavens, 
for the equinox to pass the twelfth part of the dial, or from one constella- 
tion to the next, will require a period of more than two thousand years. 
Since the astronomer first noted the position of this hour hand on the dial 
of the stars, but one of its mighty hours of two thousand years, has 
rolled away. In case any record could be found, any chiselled block of 
granite, exhibiting the place of the equinox among the stars, at its date, 
no matter if ten thousand years had elapsed, we can reach back with cer- 
tainty and fix the epoch of the record. 

No such monument has ever been found ; but there are occasional 
notices of astronomical phenomena, found among the Greek and Roman 
poets, which at least give color to conjecture. Virgil informs us that 
" the White Bull opens with his golden horns the year." 

" Candidus auratis aperit cum eornibus annum,' 
"Taurus." 



44 STRUCTURE OF THE UNIVEUSE. 

This statement we know is not true, if applied to the age in which the 
poet wrote, and seems to be the quotation of an ancient tradition. If this 
conjecture be true, this tradition must have been carried down the stream 
of time for more than two thousand years, to reach the age in which the 
poet wrote. Although these conjectures are vague and uncertain, the fre- 
quent allusions to the constellations of the zodiac, in the old Hebrew 
Scriptures, and in the works of all ancient writers, sufficiently attest the 
extreme antiquity of these arbitrary groupings of the stars. 

In taking leave of the primitive ages of astronomy and in entering on 
that portion of the career of research and discovery whose history has 
been preserved, let us pause for a moment and consider the position oc- 
cupied by the human mind at this remarkable epoch. 

Thus far the eye had done its work faithfully. Through long and 
patient watching, it had revealed the facts, from which reason had wrought 
out her great results. The stars grouped into constellations glittered in 
the blue concave of a mighty sphere, whose centre was occupied by the 
earth. Within this hollow sphere, sun, moon and planets, kept their ap- 
pointed courses, and performed their ceaseless journeys. Their wander- 
ings had been traced, — their pathway in the heavens was known, — their 
periods determined, — the inclinations of their orbits fixed. So accurately 
had the eye followed the sun and moon, that it had learned to anticipate 
their relative positions, their oppositions and conjunctions, till reaching 
forward, it had robbed the dread eclipse of its terrors, and had learned to 
hail its coming with delight. The pathway of the sun and moon among 
the stars had been scanned and studied, until their slowest changes had 
been marked and measured. 

Such were the rich fruits of diligence and perseverance which descended 
from the remote nations of antiquity. With the advantage of these great 
discoveries, and the experience of preceding ages, it is natural to expect 
rapid progress, when science found its home among the bold, subtle, and 
inquisitive Greeks. He who entertains this expectation will meet with dis- 
appointment. Not that investigations were less constantly or perseveringly 
conducted, — not that less perfect means were employed, or less powerful 
talent consecrated to the work ; but because a point had been reached of 
exceeding difficulty. The era of discovery from mere inspection was 
rapidly drawing to a close. It was an easy matter to count the days from 
full moon to full moon, to watch a planet as it circled the heavens, from 
a fixed star until it returned to the same star again, to mark its stopping, 
its reversed motion, and its onward goings ; but it was a far different 
matter to rise to a knowledge of the causes of these stations and retrogra- 
dations, and to render a clear and satisfactory account of them. The 
problem now presented, was to combine all the facts treasured by antiq- 
uity, all the movements exhibited in the heavens, and reduce them to 
simplicity and harmony. The Greek philosophers, from Plato down to 



MOTIONS OF THE HEAVENLY BODIES. 46 

the extinction *j the last school of philosophy, recognized this to be the 
true problom, ^ ^ essayed its solution, with an energy and pertinacity 
worthy of the highest admiration. 

Let us not examine the causes which arrested the progress of astronomi- 
cal discovery and held back the mind for a period of more than two thou- 
sand years. Surrounded as we are by the full blaze of truth, accustomed 
to the simplicity and beauty which now reign everywhere in the heavens, 
we find it next to impossible to realize the true position of those brave 
minds, which, enveloped in darkness, deceived by the senses, fettered by 
prejudice, struggled on and finally won the victory, whose fruits we enjoy. 

The most careful and philosophical examination of the heavens seemed 
to lead to the admitted truth, that the earth was the centre of all celestial 
motion. In the configuration of the bright stars there was no change. 
From age to age, from century to century, immovably fixed in their rel- 
ative positions, they had performed their diurnal revolutions around the 
earth. They were ever of the same magnitude, of the same brilliancy. 
How impossible was this, on any hypothesis, except that of fixed central 
position of the earth. Leaving the fixed stars, an examination of the mo- 
tions of the sun and moon — their nearly uniform velocity — their invariable 
diameters in all portions of their orbits, demonstrated the central position 
of the earth with reference to them. To shake a faith thus firmly fixed, 
sustained by the evidence of the senses, consonant with every feeling of 
the mind, accordant with fact and reason, required a depth of research, 
and the development of new truths, only to be revealed after centuries of 
observation. 

Every effort, then, to explain the celestial phenomena, started with the 
undoubted fact, that the earth was the centre of all motion. Thus far, the 
mind had not reached the idea of apparent motion. If the moon moved, 
so equally did the sun. There was exactly the same amount of evidence 
to demonstrate the reality of the one motion, as the other ; neither were 
doubted. It would have been unphilosophical to reject the one, without 
rejecting the other. 

The centre of motion once determined, the nature of the curve de- 
scribed was so obviously presented to the eye, that it seemed impossible 
to hesitate for one moment. The circle was the only regular curve known 
to the ancients. Its simplicity, its beauty and perfection, would have in- 
duced its selection, even had there been a multitude of curves from which 
to choose. Its curvature was ever the same. It had neither beginning 
nor end. It was the symbol of eternity, and admirably shadowed forth 
the eternity of the motions to which it gave form. As if these consider- 
ations had required confirmation, every star and planet, the sun and 
moon, all described circles, in their diurnal revolution, and it seemed im- 
possible to doubt that their orbitual motions were performed in the same 
beautiful curve. In truth, observation confirmed this conjecture ; and 



43 8TBUCTUBE OF THE UNIVERSE. 

'ne orbits of all the moving bodies, when projected on the concave heav- 
ens, were circles. That this curve, then, should have been adopted with- 
out doubt or hesitation, is not to be wondered at. It came therefore, to 
be a fixed principle, that in all hypotheses devised to explain the phenom- 
ena of the heavens, circular motion and circular orbits, alone could be 
employed. 

To these great principles, of the central position of the earth, and the 
circular orbits, we must add that of the earth's immobility. This doctrine 
was undoubtedly sustained by the evidence of all the senses which could 
give testimony. No one had seen it move, — had heard it move, — had felt 
it move. How was it possible to doubt the evidence of the eye, the touch, 
the ear? Here, then, was another incontrovertible fact, which even the 
most skeptical could not doubt, and which laid at the foundation of all 
effort to resolve the problem under examination. 

"With a full knowledge and appreciation of these facts, we are prepared 
to enter upon an examination of the career of astronomy, up to the time 
when all darkness disappeared before the dawning of a day which should 
never end. The early Greek philosophers, little fitted by nature for 
close and laborious observation, rather chose to gather in travel the wis- 
dom which was garnered up in the temples, and among the priests of 
Egypt, and India. Returning to their native country, they theorized on 
the facts they had learned, and taught doctrines, which found their only 
support in trains of fanciful or specious reasoning. Thus we find Pytha- 
goras mingling the great discoveries of antiquity with theories the most 
>ague and visionary. While gleams of truth flash occasionally through 
the darkness of his doctrines, they seem but fortunate guesses. His views 
were sustained by no solid argument, and rapidly sunk into forge tfulness. 
This philosopher is said to have fixed the sun in the centre of his plane- 
tary system, and to have taught the revolution of the earth in an orbit ; 
but to sustain this bold conjecture, the only reason assigned, was, that 
fire which composes the sun, was more dignified than earth, and hence 
should hold the more dignified position in the centre. We are not sur- 
prised that Hipparchus and Ptolemy, the true astronomers among the 
Greeks, should have rejected a doctrine sustained by so futile and absurd 
a reason. Nicetas, a follower of Pythagoras, is said to have gone farther 
than his master, and to have adopted the idea that the revolution of the 
heavens, was an appearance produced by an actual rotation of the earth 
on an axis, once in twenty-four hours. This extraordinary and almost 
prophetic announcement, unfortunately was not sustained by any solid 
argument. It was regarded as a vain dream, and soon was lost in obliv* 
ion. 

A crowd of theoretic philosophers filled for a long time the school of 
Greece, contributing little to science, and diverting the mind from the 
only train of research which could lead to any true results. At lengt ha 



MOTIONS OF THE HEAVENLY BODIES. 47 

philosopher arose who restored investigation to its legitimate channel, 
Hipparchus, abandoning, for the present, all vain effort to explain the 
phenomena of the heavens, gave himself up to close, continuous and accu- 
rate observation. He began with the movements of the sun in his annual 
orbit. By the construction of superior brazen circles, he measured the 
daily motion of the sun during the entire year. He confirmed the discov- 
ery of the ancients, of the irregular or unequal progress of this luminary, 
and fixed that point in the sun's orbit where it moved with greatest 
velocity. Year after year, did this devoted astronomer follow the sun, 
until finally he discovered that the point on the orbit, where its motion 
was swiftest, did not remain fixed, but was advancing in each revolution, 
at a very slow rate along the orbit. Having thus demonstrated and 
characterized the irregularity of the sun's motion, he directed his atten- 
tion to minute examinations of the moon, and reached results precisely 
similar. From these discoveries, it became manifest, that in case the 
motions of the sun and moon were circular and uniform, the earth did not 
occupy the exact centres of their orbits ; for on this hypothesis any irreg- 
ularity of motion would have been impossible. Here was a point gained. 
The exact central position of the earth was disproved in two instances, 
and even the amount of its eccentricity, or distance from the true centre, 
determined. Retaining the circular and uniform motion of the sun and 
moon, the discovered irregularities were tolerably well represented by the 
eccentric position of the earth, from whose surface these motions were 
measured. 

While pursuing these important researches, Hipparchus resolved upon 
a work of extraordinary difficulty, which had never before been attempted 
and which fully attests the grandeur and sagacity of his views. This en- 
terprise was nothing less than numbering the stars and fixing their posi- 
tions in the heavens. This he actually accomplished, and his catalogue 
of 1081 of the principal stars, is perhaps the richest treasure which the 
Greek school has transmitted to posterity. We cannot too much admire 
the disinterested devotion to science, which prompted this great under- 
taking, and the firmness of purpose which sustained the solitary observer, 
through long years of toil. It was a work for posterity, and could yield 
to its author no reward during his life. Conscious of this, his resolution 
never faltered, and grateful posterity crowns his memory with the well- 
earned title of Father of Astronomy. The noble example thus set by 
Hipparchus, was not lost on Ptolemy, justly the most distinguished 
among his immediate successors. An ardent student, a close observer, a 
patient and candid reasoner, Ptolemy collected and digested the discov- 
eries and theories of his predecessors, and transmitted them, in connection 
with his own, successfully to posterity. Rejecting the absurd doctrine 
of the solid crystal spheres of Eucloxus, and the unsustained notions of 
Pythagoras, this bold Greek undertook the resolution of the great problem 



48 STRUCTURE OF TEE UNIVERSE. 

whioh Plato had long before presented, and to accomplish which, go many 
unsuccessful efforts had been made. 

After a careful examination of all the facts and discoveries, which the 
world then possessed, adding his own extensive observations, Ptolemy 
promulged a system which bears his name, and which endured for more 
than fourteen hundred years. He fixed the earth as the great centre, 
about which the sun, the moon, the planets, and the starry heavens re- 
volved. Retaining the doctrine of uniform circular motion, he accounted 
for the irregularity in the movements of the sun and moon by the eccen- 
tric position of the earth in their orbits. — To explain the anomalous move- 
ment of the planets, he devised the system of cycles and epicycles. Every 
planet moved uniformly in the circumference of a small circle, whose 
centre moved uniformly in the circumference of a large circle, near whose 
centre the earth was located. By this ingenious theory, it was shown 
that a planet moving in the circumference of its small circle might appear 
to retrograde, to become stationary, and finally to advance among the 
fixed stars. Thus were all the phenomena known to the Greek astron- 
omer, so satisfactorily accounted for, that it even became possible from 
this singular theory, to compute tables of the planetary motions, from 
which their places could be predicted with such precision, that the error 
if any existed, escaped detection by the rude instruments then in use. 

While the explanation of the celestial phenomena had constituted the 
principal object of the Greek astronomers, some rude efforts were com- 
menced to determined the magnitude of the earth, and the relative dis- 
tances of the sun and moon. The process adopted by Eratosthenes, two 
thousand years ago, to determine the circumference of the earth, and its 
diameter, is essentially the same now employed by modern science. The 
results reached by the Greek astronomer, owing to an ignorance of the 
exact value of his unit, are lost to the world. 

When astronomy was banished from Greece, it found a home among 
the Arabs. When darkness and gloom wrapped the earth through ten 
long centuries, and human knowledge languished, and art died, and 
genius slumbered, it is a remarkable fact, that astronomy during that long 
period of ignorance, instead of being lost, was actually slowly advancing, 
and when the dawn of learning once more broke on Europe, the astron- 
omy of the Greeks, improved by the Arabs and the Persians, was preserved 
in the great work of Ptolemy, and transmitted to posterity. 

It is true that no change had been wrought in the Greek theory, but 
observations had been multiplied and slow changes measured, which pre- 
pared the way for the discoveries which were soon to succeed. On the 
revival of learning in Europe, the literature and science of the Greeks 
and Romans rapidly spread, and gained an astonishing ascendancy over 
the human mind. Indeed, theirs was the only science, the only wisdom. 
Time honored, and venerable with age, the philosophy of Aristotle, the 



MOTIONS OF THE HEAVENLT BODIES, 49 

geometry of Euclid, and the astronomy of Ptolemy, filled the colleges and 
universities, and fastened itself upon the age, with a tenacity, which per- 
mitted no one to question or doubt, and which seemed to defy all further 
progress. — Such was the state of science and the world, when Copernicus 
consecrated his genius to the examination of the heavens. 

To a mind singularly bold and penetrating, Copernicus united habits of 
profound study and severe observation. Deeply read in the received 
doctrines of science, he examined with the keenest interest, every hint 
which the philosophers of antiquity had left on record concerning the 
system of nature. For more than thirty years he watched, with unceasing 
perseverance, the movements of the heavenly bodies. By the construc- 
tion of superior instruments, he compared the observed places of the sun, 
moon and planets, with their positions computed from the best tables 
founded on the theory of Ptolemy. The hypothesis of uniform circular 
motion, had originally been adopted, to preserve the simplicity of nature 
and with true philosophy. But as one irregularity after another had been 
discovered in the movements of the heavenly bodies, each of which must 
be explained on the circular hypothesis, one circle had been successively 
added to another, eccentrics and epicycles, equants and differents, until to 
preserve simplicity, the system had grown to the most extravagant com- 
plexity. The primitive idea of simplicity was a just one, founded in 
nature, and adopted in reason. But after thirty years of vain effort to 
harmonize the phenomena of the heavens with the theory of Ptolemy, 
after entangling himself in a maze of complexity in his effort to preserve 
simplicity, Copernieus was at last driven to doubt, and doubt soon grew 
into disbelief. By a close examination of the motions of Mercury and 
Venus, he found that these planets always accompanied the sun, partici- 
pated in its movements, and never receded from it except to limited dis- 
tances. The uniformity of their oscillations, from the one side to the other 
of the sun, suggested their revolution about that luminary, in orbits, 
whose planes passed nearly through the eye of the observer. The Egyp- 
tians had reached to this doctrine, had communicated it to Pythagoras, 
who taught it to his countrymen, nearly two thousand years before the 
time of Copernicus. 

If then simplicity imperiously demanded the abandonment of the earth 
as the great centre of motion, in the search for a new centre, a multitude 
of circumstances pointed to the sun. It was the largest and most bril- 
liant of all the heavenly bodies. It gave light to the moon and planets. It 
gave life to the earth and its inhabitants. It was certainly accompanied 
by two satellites, and above all, it was so related to the earth, that if 
motion in the one was abandoned, it must instantly and without a mo- 
ment's hesitation, be . transferred to the other. Long did the philosopher 
hesitate, perplexed with doubts, surrounded by prejudice, embarrassed 
with difficulties, but finally rising superior to every consideration save truth, 

4 



5# 8BTUCTURE OF THE UNIVERSE. 

he quitted the earth, swept boldly through space, and planted himself up- 
on the sun. With an imagination endowed with the most extraordinary 
tenacity, he carried with him all the phenomena of the heavens, which 
were so familiar to his eye, while viewed from the earth. A long train 
of investigation was now before him. He commences with his now dis- 
tant earth. Its immobility is gone — he beholds it sweeping round the 
heavens in the precise track once followed by the sun. The same con- 
stellations mark its career, the same periodic time, the same inequalities 
of motion : all that the sun has lost the earth has gained. 

Thus far the change had been without results. He now gives his at- 
tention to the planets. Here a most beautiful scene broke upon his senses. 
The complex wanderings of the planets, their stations, their retrograde 
motions, all disappeared, and he beheld them sweeping harmoniously 
around him. The earth, deprived of her immobility, started in her orbit, 
joined her sister planets, and gave perfection to the system. The os- 
cillations of Mercury and Venus were converted into regular revolutions, 
still holding their places nearest to the sun ; then came the earth, next 
Mars, and Jupiter, and last of all Saturn away in the distance, slowly 
pursuing his mighty orbit. All were moving in the same direction, their 
paths filling the same belt of the heavens. 

Charmed with this beautiful scene, the philosopher turns to an examina- 
tion of the moon. Was she, too, destined to take her place among the 
planets. A short investigation revealed her true character. She conld 
not be a planet revolving about the sun interior to the earth's orbit, for 
if so she would have imitated the oscillations of Mercury and Venus. 
She was not a planet revolving around the sun, exterior to the orbit 
of the earth, for in that case she must have imitated the stations and 
retrogradations of Mars, Jupiter, and Saturn. The invariability of her 
diameter as seen from the earth, joined to these considerations, established 
the fact of her secondary character, and like a favorite minister who ac- 
companies his dethroned monarch in his exile, so did the faithful moon 
cling to the earth and follow it in its wanderings through space. 

Such is the beautiful system wrought out by the great Polish philoso- 
pher. Far from perfect, it was founded in truth, and although improvement 
might and must come, revolution could never shake its firm foundation. — 
While the more prominent irregularities in the planetary motion, were re- 
moved by constituting the sun the centre of motion, there yet remained 
an increase and decrease in the orbitual velocities of all the planets, now 
including the earth among the number, which were inexplicable. The 
planets did not revolve, then, in circles whose exact centre was occu- 
pied by the sun. The moon's orbit was not a circle, whose exact centre 
was the earth ; and to explain these unfortunate irregularities, Copernicus 
clinging to circular motion, as the world had done for 2000 years, was 
driven to adopt the same expedients which characterized the theories of 



MOTIONS OF THE HEAVENLY BODIES, &1 

Ptolemy : the eccentric and epicycle were fastened upon the new sys- 
tem of astronomy. Yet another difficulty embarrassed the mind of Co- 
pernicus. In giving to the earth a rotation on its axis once in twenty- 
four hours, he explained the apparent revolution of the starry heavens. 
This axis of rotation, it was readily seen, must ever remain parallel to 
itself in the annual revolution of the earth in its orbit. Being in this way 
carried round such a vast circumference, the prolongation of the axis 
ought to pierce the northern heavens in a series of points which would 
form a curve so large as not to escape detection. But no such curve ap- 
peared, the north pole of the heavens, scrutinized with the most delicate 
instruments, preserved its position, immovably throughout the entire rev- 
olution of the earth in its orbit, and to escape from this difficulty there 
was no alternative but to admit that the distance of the sphere of the 
fixed stars was so great that the diameter of the earth's orbit, equal to 
200,000,000 of miles was absolutely nothing, when compared with that 
mighty distance. 

Under these circumstances, it is not wonderful that Copernicus should 
have promulgated his system with extreme diffidence and only after long 
delay ; indeed his great work, setting forth his doctrines, was never read by 
its author in print, and only reached him in time to cheer his dying mo- 
ments. 

We cannot then be surprised, that the new system was received with 
doubt and distrust, or rather that it was for a long while absolutely re- 
jected. — The progress of truth is ever slow, while error moves with rapid 
pace. The reason is obvious. — Error is seized by a class of minds, which 
asks no evidence ; while the searchers for truth, adopt it only after the 
most deliberate examination. 

But the revolution had been commenced. A few bold minds were 
struck with the simplicity and beauty of the conjectures of Copernicus ; 
and when the exigencies of the age demand genius, it seems to rise 
spontaneously. The mind had persevered in a system founded in reason, 
and which nothing short of this very perseverance could have demonstrated 
to be erroneous. Like the traveler, who is uncertain which of two roads 
to take, he reflects, reasons, and decides, and even if his choice be a wrong 
one it would be folly to stop before fully convinced that he had chosen 
erroneously. 

But the mind is once again in the path of truth ; and after wandering 
twenty long centuries in darkness, which grew deeper and deeper, the 
change from darkness to light gives vigor to its movements, and its future 
achievements are destined to be rapid and glorious. 

Here let us pause for a moment, on the boundary which divides ancient 
from modern science, and glance at the collateral circumstances which 
were found to modify and retard the investigations which had commenced. 
The old doctrines of philosophy and astronomy, hzd become intimately in* 



52 STRUCTURE OF THE UNIVERSE. 

terwoven with human society. Ptolemy, and Plato, and Aristotle, were 
regarded with a sort of reverential awe. Even the church, not following, 
but leading the world in this profound respect for ancient philosophy, 
pronounced the doctrines of Ptolemy in accordance with the revelations 
of scripture, and girdled them with the fires of persecution, through which 
alone their sacredness could be attacked. Thus entrenched, and defended 
by prejudice, by society and by religion, none but the most daring spirit 
would enter the conflict against such unequal odds. Conscious of these 
difficulties, Copernicus had wisely avoided collision, and gave his doctrines 
to the world with such caution as not to provoke attack. But this armed 
neutrality could not long endure. If the new doctrine were founded in 
error, left to itself it would never advance, and would soon quietly sink 
into oblivion. On the contrary, should it prove to be based upon truth, 
no power could arrest its progress, or stay its development. The con- 
test must come sooner or later, and demanded in those who should battle 
for the truth the rarest qualities. 

Copernicus had merely commenced the examination of his bold conject- 
ure. A life-time was too short to accomplish more. He had transferred 
the center of motion from the earth to the sun, and rested the truth of his 
hypothesis on a diminished complexity in the celestial phenomena. In 
case the true centre had been found, it now remained to determine the 
exact curves in which the planets revolved, the laws regulating their 
motion, and the nature of the bond which it was now suspected, united 
the planetary worlds into one great a system. The resolution of these pro- 
found questions was reserved for Kepler, who has without flattery been 
termed the legislator of the heavens, and who has earned the reputation 
of being first in fact and first in genius among modern astronomers. He 
united in themost perfect manner, all the qualifications of a great discoverer. 
Ardent, enthusiastic, and subtle, he pursued his investigations with a keen 
and restless activity. Patient, .laborious, and determined, difficulties 
shrunk at his approach, and obstacles melted before him. Unprejudiced 
and pious, he sought for truth in the name and invoking ever the guidance 
of the great Author of truth. If his theories were not actually deduced 
from facts, when formed, no test was too severe, and nothing short of a 
rigid coincidence with fact could satisfy the exacting mind of this wonder- 
ful genius. Realizing fully the difficulty and importance of the researches 
before him, once commenced, his perseverance knew no limit, and the 
fertility of his imagination was utterly inexhaustible. 

Such was the man to whom the interests of science at this critical juncture 
were committed. Having adopted as an hypothesis, the central position 
of the sun, and the revolution of the earth and planets around this centre* 
he determined to discover the true nature of the planetary orbits, and 
find if possible, some single curve which would explain the orbitual 
motions of the celestial bodies. To accomplish this difficult enterprise, 



MOTIONSOF THE HEAVENLY BODIES. 53 

Kepler wisely'determined to confine his efforts and investigations to one 
single planet, and Mars was selected as the subject for experiment. He 
commenced by a rigorous comparison between the observed places of the 
planet and those given by the best tables which could be computed by the 
circular theory. Sometimes the predicated and observed places agreed 
well with each other, and hope whispered that the true theory had been 
found ; but pursuing the planet onward in its sweep around the sun, it 
would begin to diverge from its theoretic track, its distance would increase 
until it became evident that the theory was false, and must be abandoned. 

Nothing daunted, the ardent philosopher consoled himself with the 
thought, that among all possible theories which the mind could frame, 
one had been stricken from the list, and a diminished number remained 
for examination. This was a new mode of research, and in case the 
number of theories was not too great, and the patience of the philosopher 
sufficiently enduring, a time would come, sooner or later, when success 
must reward his labors. Thus did Kepler toil on subjecting one hypothesis 
after another to the ordeal of rigid experiment, until no less than nine- 
teen had been tested with the utmost severity and all were rejected. 
Eight years of incessant labor had been devoted to this examination. He 
had exhausted every combination of circular motion which the fertility 
of his imagination could suggest. They had all utterly failed. — The charm 
was ended, and he finally broke away from the fascination of this beautiful 
curve, which for five thousand years had so bewildered the human mind, 
and boldly pronounced it impossible to explain 'the planetary motions 
with any circular hypothesis. This at least was a great negative triumph. 
If he had not found the curve in which the planets revolved, he had 
found what it could not be, and released from all future embarrassment 
from eccentrics and epicycles, he now pursued a lofty and independent 
train of investigation. 

Leaving forever the circle, the next simplest curve is called the ellipse, 
an oval figure, which when but little flattened very nearly resembles the 
circle in form but enjoys very different properties. All diameters of a 
circle are equal. The diameters of an ellipse are unequal. The centre 
of the circle is equally distant from all points on the circumference. No 
such point exists in the ellipse ; but two curious points are found on its 
longest diameter, possessing the remarkable property of having the sum 
of the lines joining them with any point of the curve constantly equal to 
the longest diameter. Each of these points is called a focus. This beau- 
tiful curve, with its singular properties, had been discovered by the Greek 
mathematicians ; but not remarking its use in nature, it had hitherto 
been regarded only as an object of amusing speculation. To this curve 
did Kepler apply, when driven from the circular hypothesis, and again 
commenced his system of forming hypotheses, and hunting them down, as 
he termed his scrutinizing process. As in the circular hypothesis the sua 



54 STBUCTURE OF THE UNIVERSE. 

had at first been located in the centre, so in commencing the elliptic 
theory the centre of the longest diameter was made the centre of motion. 
Buoyant with hope, the astronomer sets out to follow the planet around 
its elliptic orbit ; but although for a short distance its movements were 
Avell represented, it finally broke away from the elliptic track, and bid 
defiance to the central hypothesis. But Kepler was not in the least 
disheartened with this first effort. — He now shifts the sun to the focus of 
the ellipse, constructs his orbit, starts once more on the track of the 
planet, watches it as it sweeps onward around the sun, the elliptic orbit 
holds it as it moves farther and still farther. — Half its revolution is per- 
formed and there is no diverging, onward it flies, — the goal is won. — 
Triumph crowns the philosopher, the orbit is found! 

Thus was accomplished one of the most important discoveries which 
the mind had ever reached. The elliptic orbit of Mars rapidly led to 
those of the other planets, and to that of the moon, and Kepler proclaimed 
to the world his first great law, in the following language : Planets revolve 
in elliptic orbits about the sun, which occupies the common focus of all these 
orbits. 

This law swept forever from the heavens and from astronomy those 
complications which had stood the test of centuries, nay of thousands of 
years. Their mysterious power was paralyzed by this single touch of the 
enchanter's wand, and they fled from the skies. The circle was as simple 
and beautiful as ever, but its divine character was gone, and the gods or 
angels who had so long held their abodes in the planets were exiled from 
their homes. The dawn of modern science broke in beauty on the world. 

Kepler having been so signally rewarded by this great discovery, now 
turned his attention to an investigation of the first importance, one indeed 
which was indispensably necessary to render his first discovery available. 
As the planets were now known to revolve in ellipses, and as their motion 
was found by observation to be unequal in different parts of their orbits, 
it became a matter of the first consequence to ascertain some simple law 
regulating the orbitual motion, and by means of which a planet might be 
readily followed, and its places computed. To detect this law, in whose 
existence Kepler seems to have entertained the most unwavering faith, a 
figure was drawn representing the orbit of Mars, the sun occupying one 
of the foci of the curve. On the circumference of this curve the places 
of the planets were marked down as observation had determined them ; 
and here commenced a series of examinations which finally led to the 
knowledge of the second great law of the planetary motions, which may 
be thus announced. If a line be drawn from the centre of the sun, to any 
planet, this line as it is carried forward by the planet will sweep over equal 
areas in equal portions of time. — This law accorded in the most perfect 
manner with fact, and gave at once the power of following, and from tht. 
mean motion, computing the place of any planet ; a triumph which all the 
complexity of older systems had failed ever to accomplish. 



MOTIONS OF THE HEAVENLY BODIES. 55 

Any other mind less adventurous than that of Kepler, might have been 
satisfied with these two great discoveries. The precise curves described 
by the planets and a law regulating their motions in their orbits, sufficed 
to render all the phenomena of the heavenly bodies not only explicable, 
but susceptible of accurate prediction. — There seemed nothing more to be 
added. — Kepler did not think so. He conceived the idea that the solar 
system was not a mere assemblage of isolated planets revolving about a 
common centre, but a great associated system, in which some common 
bond of union existed, which once found, would present the solar system 
in a new and true light. 

This bond he believed existed in some hidden relation between the 
times occupied by the planets in describing their orbits, and their distances 
from the sun. In the history of this remarkable research, we are pre- 
sented with one of the brightest examples of the fruits of perseverance. 
If some superior power, some spirit from a brighter world, had revealed 
to the mind of Kepler the actual existence of some relation between the 
planet's periods and distances, and had proposed to him to discover this 
hidden law, there would have been a definite object before the astrono- 
mer, and to have persevered in the pursuit of this object, would have 
been within the limits of probability, even if a lifetime were exhausted in 
fruitless efforts. But to excite in his own mind a faith sufficiently strong 
in the existence of a law of which there existed not the slightest evidence, 
and to have persevered in its research for seventeen long years of laborious 
effort, seems almost incredible. 

There is an immense difference between the pursuit which resulted in 
the discovery of the first two laws of Kepler, and the third one. In 
seeking for the curve described by the planets, it was looking for that, 
which must have an existence ; and in tracing the law of a planet's 
motion, it was absolutely impossible to follow a planet, or predict its po- 
sitions, without such a law. But in seeking for a bond of union among 
the planetary periods and distances, it was a search for that, which it was 
believed had no existence, except in the wild imagination of this ex- 
traordinary philosopher. The history of mind scarcely furnishes an ex- 
ample in any degree paralleled, if we except perhaps the heroic fortitude 
which marked the career of Columbus. — Yet even the great Genoese was 
in possession of solid facts on which to base his reasoning. He saw evi- 
dences of the existence of another hemisphere, which the superficial could 
never realize. Kepler, more bold, more grand, more sublime, dreamed of 
nothing less than a brotherhood of worlds, a mighty and magnificent 
scheme of vast revolving orbs. Should success crown his efforts, the 
most brilliant results would follow. The distance of a single planet from 
the sun once obtained, and the periodic time of all being known, the dis- 
tances might then be found for each individual in the entire system, 
without even directing an instrument to the heavens.*. Here Jheniwas^a! 



56 8TEUCTURE OF THE UNIVERSE. 

prize to reach which no time, or pains, or labor could be misapplied. Its 
return would be a hundred-fold. 

But where was the prize to be sought ? Even admitting that some 
common bond did bind the circling worlds into one harmonious system, 
did it exist in some hidden relation between their periods of revolutions, 
their distances, their magnitudes, their densities ? or was it to be sought 
in some analogy between the distances and periodic times? After long 
and deliberately pondering this great problem, Kepler decided that the 
strongest probability suggested that the distances of the planets and their 
periods of revolution, would in some way contain the mysterious bond of 
union. Here then did this daring mind concentrate its energies ; and his 
purpose once fixed, he marches steadily forward in his research with a 
courage which no defeat could daunt, and a perseverance which knew no 
limit but success. 

Before announcing the final result, let me explain two terms employed 
in its statement. The square of any quantity results by multiplying it 
by itself. The cube comes from multiplying the square by the number. 
The square of a planet's period, or the cube of its distance, are known the 
moment we know the period, and distance, by applying the simple rules 
of arithmetic. After Kepler had exhausted all simple relations between 
the periods and distances of the planets, in no degree shaken in his lofty 
faith, he proceeded to try all possible relations between the squares of 
the periods and distances ; but with as little success. Nothing daunted, 
he proceeded to investigate the possible relations between the cubes of 
the periods and distances. Here again he was foiled; no law exhibited 
itself. — He returned ever fresh to the attack, and now commenced a series 
of trials involving the relations between the simple periods and the 
squares of the distances. Here a ray of hope broke in upon his dim and 
darkened path. 

No actual relation existed, yet there was a very distant approixmation, 
enough to excite hope. — He then tried simple multiples of the periods 
and the squares of the distances — all in vain. He finally abandoned the 
simple periods and distances, and rose to an examination of the relations 
between the squares of these same quantities. — Gaining nothing here, he 
rose still higher, to the cubes of the periods and distances ; — no success, 
until finally he tried the proportion existing between the squares of the 
periods in which the planets perform their revolutions and the cubes of 
their distances from the sun. — Here was the grand secret, but, alas ! in 
making his numerical computations, an error in the work vitiated the 
results and with the greatest discovery which the mind ever achieved in 
his very grasp, the heart-sick and toil-worn philosopher turned away 
almost in despair from his endless research. 

^Months rolled round, and yet his mind with a sort of keen instinct, 
wimldlrecurlagaini audi again to this last hypothesis. Guided by some 



MOTIONS OF THE HEAVENLY BODIES. 67 

Mnd angel or spirit whose sympathy had been touched by the unwearied 
zeal of the mortal, he returned to his former computations, and with a 
heaving breast, and throbbing heart, he detects the numerical error in hia 
work, and commences anew. The square of Jupiter's period is to the 
square of Saturn's period as the cube of Jupiter's distance is to some 
fourth term, which Kepler hoped and prayed might prove to be the cube 
of Saturn's distance. With trembling hand, he sweeps through the maze 
of figures ; the fourth term is obtained ; he compares it with the cube of 
Saturn's distance. — They are the same ! — He could scarcely believe his 
own senses. He feared some demon mocked him. — He ran over the work 
again and again. — He tried the proportion, the square of Jupiter's period 
to the square of Mars' period as the cube of Jupiter's distance to a fourth 
term, which he found to be the cube of the distance of Mars. — Till fin- 
ally full conviction burst upon his mind : he had won the goal, the strug- 
gle of seventeen long years was ended, God was vindicated, and tha 
philosopher in the wild excitement of his glorious triumph, exclaims : 

" Nothing holds me. I will indulge my sacred fury ! If you forgive 
me I rejoice ; if you are angry I can bear it. The die is cast. The 
book is written, to be read either now, or by posterity, I care not which. 
— It may well wait a century for a reader, since God has waited six 
thousand years for an observer ! " 

More than two hundred years have rolled away since Kepler announced 
his great discoveries. Science has marched forward with swift and re- 
sistless energy. The secrets of the universe have been yielded up under 
the inquisitorial investigations of god-like intellect. The domain of the 
mind has been extended wider and wider. One planet after another has 
been added to our system ; even the profound abyss which separates us 
^om the fixed stars has been passed, and thousands of rolling suns have 
een described, swiftly flying or majestically sweeping through the 
hronged regions of space. But the laws of Kepler bind them all,— 
satellite and primary — planet and i un — sun and system — all with one 
accord, proclaim in silent majesty* th 3 triumph of the hero philosopher. 



LECTURE IV. 

DISCOVERY OF THE GREAT LAWS OP MOTION AND GRAVITATION. 

The remarkable discoveries which, had rewarded the researches of 
Kepler, confirmed in the most perfect manner the doctrines of Copernicus, 
flowing as they did from his prominent hypothesis, the central position of 
the sun. Having reached to the true laws of the planetary motions, the 
whole current of astronomical research was changed. New methods 
were demanded, and more delicate means of observation must be brought 
into use before the data could be furnished for new discoveries. Hence- 
forward astronomy could only advance by the aid of kindred sciences. 
Mathematics, optics, and above all, mechanical philosophy, were to be- 
come the instruments of future conquests. 

The philosophy of Aristotle, though very far from deserving it, wielded 
quite as extensive an influence over the age, as did the astronomy of 
Ptolemy. It appears, indeed, that the followers of Aristotle regarded 
their master as absolutely infallible, and gave to his doctrines a credence 
so firm, that even the clearest experiments, the most undeniable evidence 
of the senses were sooner to be doubted than the doctrines of the divine 
Greek. To attack and destroy a system so deeply rooted in the prejudices 
of the age, required a mind of extraordinary courage and power, a mind 
deeply imbued with the love of truth, quick in its perceptions, logical in 
argument, and firm in the hour of trial. 

Such a mind was that of the great Florentine philosopher, Galileo 
Galilei, the senior, friend, and contemporary of Kepler. Indeed the exig- 
encies of the age seemed to have given birth to three men, whose peculiar 
constitutions fitted them for separate spheres, each of the highest order, 
each in some measure independent, and yet all combining in the accom- 
plishment of the great scientific revolution. While Tycho, the noble 
Dane, immured within the narrow limits of his little island, watching 
from his sentinel towers the motions of the stars, noting with patient and 
laborious continuity, the revolutions of the sun, moon and planets, was 
accumulating the materials which were to furnish the keen and inquisitive 
mind of Kepler with the means of achieving his great triumphs — Galileo, 
with a giant hand, was shaking to their foundations the philosophical 
theories of Aristotle, and startling the world with his grand mechanical 
discoveries. But for the observations of Tycho, Kepler's laws could not 



60 8THTTCTVRE Of TBS UmVEUSB. 

have been revealed ; — but for the magic tube of Galileo, these laws had 
been the m plus of astronomical science. Thus do we witness the rare 
spectacle of three exalted intellects, contemporaneously putting forth 
their diverse talents in the accomplishment of one grand object. The 
Dane, the German, and the Italian, divided by language and by country, 
united in the pursuit of science and of truth. 

Called to Pisa to discharge the duties of a philosophical teacher, Galileo 
was not long in detecting the extravagant philosophical errors of Aristotle, 
which had been implicitly received for more than twenty centuries. He 
continued to teach the text of his old master, but it was only to expose 
its unsound and false philosophy to his wondering and incredulous pupils. 
A desecration so monstrous, could not long escape exposure and punish- 
ment. Indeed the Florentine made no secret of his teachings. The 
Aristotelians made common cause against the young philosophical heretic, 
and he was warned to desist from his heresy. Galileo gave for answer to 
his opponents, that he was ready to relinquish his new views the moment 
they were shown by experiment to be false ; on the other hand, he de- 
manded of them equal candor, and proposed to refer the matter in con- 
troversy to the tribunal of experiment. 

Aristotle, in discussing the laws of falling bodies, affirmed the principle, 
that the velocity acquired by any falling body, was in the direct propor- 
tion of its weight ; and if two bodies of unequal weight commenced 
their descent from the same height, at the same moment, the heavier 
would move as many times swifter than the lighter, as its weight 
exceeded that of the smaller body. Galileo doubted the truth of this 
principle, and on subjecting it to the test of experiment, he saw in- 
stantly that its variation from fact was wide as it could be. The ob- 
vious character of this experiment, its freedom from all chances of de- 
ception, and the importance of the principle involved, induced the young 
philosopher to select it as the test, and to challenge his opponents to a 
public demonstration of the truth or falsehood of their old system of 
philosophy. — The challenge was accepted. The leaning tower of Pisa 
presented the most convenient position for the performance of these ex- 
periments, on which Galileo so confidently relied for triumphant demon- 
stration of the error of Aristotle ; and thither on the appointed day the 
disputants repaired, each party perhaps with equal confidence. It was a 
great crisis in the history of human knowledge. On the one side, stood 
the assembled wisdom of the universities, revered for age and for science, 
venerable, dignified, united and commanding. Around them thronged 
the multitude, and about them clustered the associations of centuries. 
On the other, there stood an obscure young man, with no retinue of 
followers, without reputation or influence, or station. But his courage 
was equal to the occasion , confident in the power of truth, his form is 
erect, and his eye sparkles with excitement. 



LAWS OF MOTION AND GRAVITATION. 61 

But the hour of trial arrives. The balls to be employed in the experi- 
ments are carefully weighed and scrutinized to detect deception. The 
parties are satisfied. The one ball is exactly twice the weight of the 
other. The followers of Aristotle maintain that when the balls are 
dropped from the top of the tower, the heavy one will reach the ground 
in exactly half the time employed by the lighter ball. Galileo asserts 
that the weights of the balls do not affect their velocities, and that the 
times of descent will be equal ; and here the disputants join issue. — The 
balls are conveyed to the summit of the lofty tower. The crowd assem- 
bles round the base — the signal is given — the balls are dropped at the 
same instant, and swift descending, at the same moment they strike the 
earth. Again and again is the experiment repeated, with uniform results. 
Galileo's triumph was complete. Not a shadow of doubt remained ; but 
far from receiving, as he had hoped, the warm congratulations of honest 
conviction — private interest, the loss of place, and the mortification of 
confessing false teaching, proved too strong for the candor of his adver- 
saries. — They clung to their former opinions with the tenacity of despair, 
and assailed the now proud and haughty Galileo with the bitter feelings 
of disappointment and hate. 

The war was now openly declared, and waged with a fierceness which 
seems to have excited the mind of the young philosopher to the most ex- 
traordinary efforts. Driven from Pisa, by the numbers and influence of 
his enemies, no suffering or danger could drive from his mind the great 
truths which his researches by experiment were constantly revealing. 
His spirit was unbroken, and in retiring from the unequal contest, he 
hurled back defiance into the face of his conquered, though triumphant 
persecutors. ' 

The mechanical investigations of Galileo, conducted with clearness and 
precision, soon led to the most important discoveries. He detected the 
law of falling bodies, and showed that the spaces described were propor- 
tional to the squares of the times ; that is, if a body fell ten feet in one 
second of time, it would fall four times as far in two seconds, nine times 
as far in three seconds, and so on for any number of seconds. He studied 
with success the subject of the composition of forces, and demonstrated 
this remarkable proposition, which lies at the very foundation of all modern 
mechanical philosophy. It may be thus stated. It a body receive an im- 
pulse, which singly would cause it to move thirty feet in a second, on the 
line of the direction of the impulse, and at the same instant another im- 
pulse be communicated in a different direction from the first, and which 
if acting alone would cause the body to move on the line of direction of 
the second impulse forty feet in one second, under the joint action of these 
two impulses the body will move in a direction easily determined from 
those of the impulsive forces, and will fly with a velocity of fifty feet in 
the first seeond of time t 



62 STEUCTURE OF THE UNIVERSE. 

Such is the universal prevalence of this beautiful proposition, that no 
falling, flying, or moving body, whether it be the rifle ball, the cannon 
shot, or the circling planet, is free from its imperious sway. Strike the 
knowledge of this great truth from existence, and the magnificent struct- 
ure which modern science has reared, falls in ruins at a single blow. It 
is founded in the simple but invariable laws of motion, and while these 
endure, this elegant discovery of the Florentine philosopher will remain 
as a monument to his sagacity and penetration. 

Possessed of such rare qualities for philosophic research, so free from 
prejudice, and withal, so candid, we cannot but inquire with interest, how 
the mind of Galileo stood affected towards the new astronomical doctrines 
of Copernicus. He had early adopted and taught the Ptolemaic system, 
and his conversion is so remarkable, and. is so characteristic of the man, 
that it cannot be omitted. A disciple of Copernicus visited the city of 
Galileo's residence, and delivered several public lectures to crowded audi- 
ences, on the new doctrines. Galileo, regarding the whole subject as a 
species of solemn folly, would not attend. Subsequently, however, in 
conversing with one who had adopted these new doctrines, the Copernican 
sustained his views with such a show of reason that Galileo now regretted 
that he had heedlessly lost the opportunity of attending the lectures. To 
make amends, he sought every opportunity to converse with the Coper- 
nicans, and remarking that they, like himself, had all once been Ptole- 
maists, and that from the doctrines of Copernicus no one had ever subse- 
quently become a follower of the old philosophy, he resolved to examine 
the subject with the most serious attention. The result may be readily 
anticipated ; the conversion was sudden and thorough, the old astronomy 
was abandoned, and the new convert became the great champion by whose 
ardor, and unconquerable zeal, the strongholds of antiquated systems 
were to be destroyed and a new and truthful one founded. 

Thus far the career of Galileo in science had been successful and bril- 
liant. He was rapidly rising in reputation and influence, when a fortu- 
nate accident revealed to the world, the application of a principle in optics 
fraught with consequences, which it is impossible to estimate. Galileo 
was informed that Jansen, of Holland, had contrived an instrument pos- 
sessing the extraordinary property of causing distant objects, viewed 
through it, to appear as distinctly as when brought near to the eye. The 
extensive knowledge which Galileo possessed of optics, immediately 
gave him the command of the important principle on which the new in- 
strument had been constructed. He saw at once the high value of such 
an instrument in his astronomical researches, and with his own hands 
commenced its construction. 

After incredible pains, he finally succeeded in constructing a telescope, 
by whose aid, the power of the eye was increased thirty fold. It is im- 
possible to conceive the intense interest with which the philosopher di- 



LA WS OF MOTION AND GBA VI TA TION, 68 

rected for the first time his wonderful tube to the inspection of the 
heavens. When we reflect that with the aid of this magical instrument 
the observer was about to sweep out through space, and to approach the 
moon, and planets, and stars, to within a distance only one- thirtieth of 
their actual distance ; that their size was to increase thirty fold, and their 
distinctness in the same ratio, it is not surprising that these wonders 
should have excited the most extravagant enthusiasm. — Galileo com- 
menced by an examination of the moon. Here he beheld, to his inexpres- 
sible delight, the varieties of her surface clearly defined, her deep cavities, 
her lofty mountains, her extensive plains, were distinctly revealed to his 
astonished vision. Having satisfied himself of the reality of these in- 
equalities of the moon's surface, by watching the decreasing shadows of 
the mountains, as the sun rose higher and higher on the moon, he turned 
his telescope to an examination of the planets. These objects, which the 
human eye had never before beheld other than brilliant stars, now ap- 
peared round and clear and sharp, like the sun and the moon to unaided 
vision. On the 8th January, 1610, the telescope was for the first time 
directed to the examination of the planet Jupiter. Its disk was clearly 
visible, of a pure and silver white, crossed near the centre by a series of 
dark streaks or belts. Near the planet, Galileo remarked three bright 
stars which were invisible to the naked eye. He carelessly noted their 
position with reference to the planet, for he believed them to be fixed stars, 
and of no special interest, except to point out the change in Jupiter's 
place. On the following night, "induced," as he says, "by he knew not 
what cause," he again directed his attention to the same planet. The 
three bright stars of the preceding evening were still within the field of 
his telescope, but their positions with reference to each other were en- 
tirely changed, and such was the change, that the orbitual motion of 
Jupiter could in no way account for it. Astonished and perplexed, the 
eager astronomer awaits the coming of the following night to resolve this 
mysterious exhibition. Clouds disappoint his hopes, and he is obliged to 
curb his impatience. — The fourth night was fair, the examination was re- 
sumed, and again the bright attendants of Jupiter had changed — his sus- 
picions were confirmed — he no longer hesitated, and pronounced these 
bright stars to be moons, revolving about the great planet as their centre 
of motion. A few nights perfected the discovery ; the fourth satellite 
was detected, and this astounding discovery was announced to the world. 
No revelation could have been more important or more opportune than 
that of the satellites of Jupiter. The advocates of the Copernican theory 
hailed it with intense delight ; while the sturdy followers of Ptolemy 
stoutly maintained the utter absurdity of such pretended discoveries, and 
urged as a sort of unanswerable argument, that as there were but seven 
openings in • the head — two ears, two eyes, two nostrils and the mouth, 
there could be in the heavens but seven planets. The more rational, 



64 STRUCTURE OF THE UNIVERSE. 

however, saw the earth, by this discovery, robbed of its pretended dignity. 
It commanded the attendance of but one moon, while Jupiter received 
the homage of no less than four bright attendants. The delighted Coper- 
nicans saw in Jupiter as a central orb and in the orderly revolution of his 
satellites, a miniature of the sun and his planets, hung up in the heavens, 
and there placed to demonstrate to all coming generations, the truth of the 
new doctrines. 

Another discovery soon followed, which it is said the sagacity of Coper- 
nicus foresaw would sooner or later be revealed to human vision. It had 
been urged by the Ptolemaists, that in case Venus revolved about the 
sun, as was asserted by Copernicus, and reflected to us the light of that 
luminary, then must she imitate exactly the phases of the moon ; when on 
the side opposite to the sun, turning towards us her illuminated hemis- 
phere she ought to appear round like the moon, while the crescent shape 
should appear on reaching the point in her revolution which placed her 
between the sun and the eye of the observer. As these changes were 
invisible to the naked eye, the objection was urged with a force which no 
argument could meet. Indeed it was unanswerable, and in case the tele- 
scope should fail to reveal these changes in Venus, the fate of the Coper- 
nican theory was forever sealed. 

The position of Venus in her orbit was computed — the crescent phase 
due to that position determined — the telescope applied, and the eye was 
greeted with an exquisite miniature of the new moon. There was the 
planet, and there was the crescent shape long predicted by Copernicus, 
received by him and his followers as a matter of faith, now become a 
matter of, sight. The doctrines of Copernicus thus received not only 
confirmation, but so far as Venus was concerned, a proof so positive that 
that no skepticism could resist. It is not my design to follow the discov- 
eries of the Florentine philosopher among the planetary orbs. These 
will be resumed hereafter, when we come to examine more particularly 
the physical constitution of the planets. I have merely adverted to those 
discoveries, which became specially important in the discussions between 
the partisans of the old and new astronomy. 

Admitting the doctrines of Copernicus, and uniting to them the great 
discoveries of Kepler, let us examine the condition of astronomical science, 
ascertain precisely the point the mind had reached, and the nature of the 
investigations which next demanded its attention. From the first of 
Kepler's laws, the figure of the planetary orbits became known, and the 
magnitude of the ellipse described b}^ any planet was easily determined. 
By observing the greatest and least distances of any planet from the sun, 
the sum of these distances gave the longer axis of the orbit ; and know- 
ing this important line, and the focus, it became a simple matter to con- 
struct the entire orbit. The line joining the planet with the sun, while the 
planet occupied its shortest or perihelion distance, gave the position of 



LAWS OF MOTION AND GRAVITATION. 65 

the axis of the orbit in space, and its plane being determined by its incli- 
nation to that of the ecliptic, nothing remained to fix in space the figure, 
magnitude and position of the planetary orbits. The next point was to 
pursue and predict the movements of these revolving bodies. This was 
readily accomplished. A series of observations soon revealed the time 
occupied by any planet in performing one complete revolution in its ellip- 
tic orbit. Knowing thus the periodic time, and the position of the plan- 
et in its orbit at any given epoch, the second law of Kepler furnished 
the key to its future movements ; its velocity in all parts of its orbit 
became known, and the mind swift and true followed the flying world in 
its rapid flight through space. It even went further ; anticipated its 
changes, and predicted its positions, with a degree of certainty only limit- 
ed by the accuracy with which the elements of its orbit had been deter- 
mined. 

The third of Kepler's laws, exhibiting the proportion between the perio- 
dic times and the mean distances of the planets from the sun, united all 
these isolated and wandering orbs into one great family. Their periods 
of revolution were readily determined by observation, and an accurate 
determination of the distance from the sun of a single planet in the group, 
gave at once the distance of all the remaining ones. The increased 
accuracy of the means of observation would render more perfect each 
successive measure of the earth's distance from the sun, and it seemed 
now that the mind might stop and rest from its arduous toil ; that scarce- 
ly anything remained to be done. The solar system was conquered, and 
the fixed stars defied the utmost efforts of human power. 

How widely does this view differ from the true one. In fact, the true 
investigation had not even commenced. A height had indeed been gained, 
from whence alone the true nature of the next great problem became 
visible, and standing upon this eminence the mind boldly propounds the 
following questions : — Why should the orbits of the planets and satellites 
be ellipses, rather than any other curve ? What power compelled them 
to pursue their prescribed paths with undeviating accuracy ? What cause 
produced their accelerated motion when coming round to those parts of 
their orbits nearer to the sun? What power held planet and satellite 
steady in their swift career, producing the most exquisite harmony of 
motion, and a uniformity of results as steady as the march of time ? 

Here I may be asked, do not such questions border on presumption ? 
Are not such inquisitorial examinations touching on the domain of God's 
inscrutable providences, and would it not be wiser to stop and rest satisfied 
with the answer to all these questions, that God, who built the universe, 
governs and sustains it by his power and wisdom ? Doubtless this answer 
is true, and in its truth man humbly finds his highest encouragement to 
attempt the resolution of the sublime questions already propounded for 
examination. Let us admit that the divine will produces all motion, 

5 



66 STRUCTURE OF THE UNIVERSE. 

speeds the earth in its rapid flight ahout the sun, guides the planets and 
their revolving moons, and poises the sun himself in empty space, as the 
great centre of life and light and heat to his attendant worlds. Is it not 
reasonable to believe that the will of the Omnipotent is exerted accord- 
ing to some uniform system, that this system is law, and that this law is 
within the reach of man ? To encourage this view the simple laws of 
motion had been already revealed, and as these must exert a controlling 
influence in our future examinations, we proceed to unfold them. 

First, then, it was discovered that if any body, situated in space and 
free to move, receive an impulse capable of giving it a velocity of ten 
feet in the first second of time, or any other velocity, it will move off in 
the direction of the impulse forever in a straight line, and with undimin- 
ished and unchanged velocity. The intensity of the primitive impulse 
determines the velocity of the body which receives it, and the one is pre- 
cisely proportioned to the other. Again, in case a moving body while 
pursuing its flight receives an impulse in a direction different from its 
primitive one, its new direction and velocity will be determined by the 
direction and intensity of the new impulse, according to the principle dis- 
covered by Galileo, and already explained. Lastly, in every revolving 
body a disposition is generated to fly from the centre of rotation. The 
body seems urged by some invisible force from the centre, and if the 
velocity be sufficiently increased, no matter how strong the bond which 
unites it to the centre, it will, in the end, be severed, and the body, freed 
from its centre, darts away in a straight line tangent to its former circle 
of revolution. This power, which urges revolving bodies from the centre 
of motion, is called the centrifugal force, and is proportioned to the squares 
of the velocity of the revolving body. Hence a cord sufficiently strong 
to hold a heavy ball revolving round a fixed centre at the rate of fifty 
feet in a second, would require to have its strength increased four-fold, to 
hold the same ball, if its velocity should be doubled. 

These simple laws, derived from a rigorous examination of those mov- 
ing bodies, subject to man's closer scrutiny, extend their sway through the 
remotest regions of sj)ace. Are these laws necessary qualities of matter ? 
Why should a body, darting away under the action of some impulsive 
force, pursue forever its undeviating direction, with undiminished ve- 
locity ? — This effect cannot arise from any necessary property or equality 
of matter. The law might have been different — the direction of the mov- 
ing body might have slowly varied — the velocity might have increased or 
decreased in any proportion, and yet the flying body, so far as we can un- 
derstand, have retained all its physical qualities and properties. No — 
Divine wisdom has selected these simple and beautiful laws from among 
a multitude, either of which might have been chosen. Stretching forward, 
therefore, to the examination of the force by which the planets are re- 
tained in their orbits, was it not reasonable to expect, that some law might 



LAWS OF MOTION AND GBAVITATION. 67 

be found, governing the application of that mysterious power, and in some 
way proportioned to the mass of the moving body, and to the orbit which 
it described in wheeling around the sun. That they were held by some 
invisible power to their centre of motion, was manifest from the fact that 
the centrifugal force, generated by the rapidity of their revolution, would 
have hurled them away from the sun, if not opposed and counterpoised 
by some equivalent power lodged in the great centre of the planetary 
orbs. Here was an object worthy the highest ambition of the human 
mind. — No matter what might be the nature of this force, whether it 
should reside in the sun, or in the planet, or in both — whether it should 
prove to be a property of matter, or the mere uniform manifestation of 
the Omnipotent will ; the discovery of its law of action would give to 
the mind the power of penetrating the darkest recesses of nature, and of 
rising to a knowledge of the profoundest secrets of the universe. 

Such is the nature of the investigation propounded to the powerful in- 
tellect of Newton. This eminent philosopher, justly regarded as the 
most extraordinary genius that ever lived, neither originated the ques- 
tion which he undertook to discuss, nor divined the law of force which he 
proposed to demonstrate. When Kepler had closed the investigations 
which led to the discovery of his three great laws, his sagacity at once 
suggested to his mind the existence of some central force, by whose 
power the planetary movements were controlled. He had watched the 
moon circling around the earth, he had scrutinized the ocean tide, whose 
crested wave seemed to rise and follow the movements of the moon, until 
he boldly announced that some invisible bond, some inscrutable power, 
united the one to the other. He even reached the conclusion, that this 
unknown force resided in the moon — that by its power the waters were 
heaved from their beds, and caused to follow the moon and imitate its 
motions. Doubtless the solid earth itself felt this mysterious power, and 
swayed to its influence ; but in consequence of the immobility of its 
particles, its effects had, thus far, escaped detection. Thus once started 
on the track, Kepler pursued the speculation. He attributed a similar 
power to the sun, and extended its controlling influence to the planets. 
He went yet farther, and conjectured that the law of this unknown force 
was such that it diminished as the squares of the distances at which it 
operated increased. That is, if the intensity of the power which it exerted 
on a planet where the distance was one hundred millions of miles from 
the sun, be counted as unity, removing the planet to double the distance, 
or to two hundred millions of miles, the sun's influence over it would be 
reduced to one-fourth of its former value. 

With Kepler this wonderful conjecture always remained without proof. 
He had placed it on record, and succeeding philosophers had treated it 
with greater or less seriousness, according to the estimate which they 
placed upon the sagacity of its author. Even if Kepler, himself, had at- 



68 STRUCTURE OF THE UNIVERSE. 

tempted the demonstration of this principle — the data were as yet wanting, 
which would have rendered its accomplishment possible. The period in- 
tervening between the time of Kepler and Newton had not been left un- 
improved. Descartes had revealed the law of centrifugal force, and by 
one of those extraordinary strokes of genius — occurring once in an age — 
had fastened the irresistible power of analysis upon geometry, which had 
given to the mind a force and rapidity in the investigation of the figure of 
curves and curvilinear motion, which had quadrupled its capacity. By re- 
peated efforts, a more accurate knowledge had been obtained of the circum- 
ference and diameter of our earth, and through this the distance of the moon 
from the earth, in the successive points of its orbit had been approximated 
with still greater precision. 

With these advantages, Newton gave the energies of his mind to the 
demonstration of that principle which had existed with Kepler as a mere 
conjecture. 

Before proceeding to develop the train of reasoning pursued by the great 
English astronomer permit me first to prepare the way by a simple and 
perspicuous exhibition of the method employed in determining the diameter 
of the earth and the distance of the moon ; two elements which figure con- 
spicuously in the demonstration about to be made, and without a knowl- 
edge of which it would have been impossible to proceed. We commence 
with a determination of the diameter of the earth. 

If an observer should start from any point on the surface of the earth in 
the northern hemisphere, and fixing his eye upon the north pole of the 
heavens, should travel directly towards that point, all the stars in the 
north would appear to rise higher above the horizon as he advanced in his 
journey. The star which occupied the point immediately above his 
head when he started, would appear gradually to decline towards the south. 
If it were possible to travel on the same great circle of the earth entirely 
around its circumference, the zenith star would appear to pursue an op- 
posite route in the heavens, and would return to its primitive position only 
on the return of the observer to his point of starting. This, however, is 
not possible. What the observer can accomplish, is this. He may travel north 
until his zenith star shall appear to have moved south by one degree, or 
the three hundred and sixtieth part of the circumference of the heavens; 
then will he have passed over the three hundred and sixtieth part of the 
entire circumference of the earth ; all these parts are of equal length, — he 
measures the one over which he has passed — multiplies its value by three 
hundred and sixty, and the result gives him the circumference of the earth, 
from which the diameter is readily deduced by the well-known proportion 
which exist between these lines. By this simple method, the diameter of 
the earth being determined, its radius is known, and we are prepared to 
explain the process by which the moon's distance may be found. 

Let us locate, in imagination, two observers at distant points on the same 



LAWS OF MOTION AKD GBAVITATlOIf. 69 

great circle of the earth, each prepared to measure the angular distance at; 
which the moon appears from the zenith point of each station ; but the 
zenith of any place is the point in which the earth's radius prolonged 
reaches the heavens, — the angular distance of the moon from the zenith will 
exhibit precisely the inclination of the visual ray drawn to the moon's 
centre with the earth's radius drawn to the place of observation ; the zenith 
distances being observed at each station, the observers knowing that part 
of the great circle of the earth by which their stations are separated, come 
together, compare observations, and construct a figure composed of four 
lines. Two of these are the radii of the earth drawn to the points of ob- 
servation. These may be laid down under their proper angle, — drawing 
from their extremities two lines, forming with the radii, angles equal to 
the moon's measured zenith distances. These represent the visual rays 
drawn to the moon ; they meet in a point which determines their length, 
and if the figure be constructed accurately, it will be found that either of 
these lines is about sixty times longer than the radius of the earth, or the 
moon's distance is about 240,000 miles. 

We now return to the examination of the great question of a central 
force, and to the discovery of its law of action. Allow me in the out-set to 
explain, with extreme simplicity, the assumed law, whose truth or false- 
hood it was required to demonstrate. If any force resided in the sun 
which could resist the centrifugal force of the planets, or in any primary 
to resist the centrifugal force of the revolving satellite, it was conjectured 
that this force would decrease in proportion as the square of the distance 
increased. In other language, if the planets were arranged at the following 
distances from the sun, the forces exerted upon them would be represented 
by the second series, thus: 

Distances, 12 3 4 5 6 &c, 

Forces, I ± i ^ i fr &c. 

The measure of the intensity of any force of attraction situated at the 
centre of the earth or sun, is accurately represented by the velocity it is 
capable of imparting to a falling body in any unit of time. Experiment 
shows that that power which causes a heavy body to fall to the earth's sur- 
face, is capable of impressing upon it a motion of about 16 feet in the first 
second of time after its fall commences. In case the force diminishes, as we 
remove the falling body farther from the centre of attraction, the law of 
diminution would manifest itself in the diminished amount of motion 
communicated to the falling body. 

Now if Newton could have carried a heavy body upward, above the earth, 
until he should gain a height above its surface of four thousand miles, he 
would then be twice as far from the centre as when at the surface of the 
earth. Dropping the heavy body, and measuring accurately the distance 
through which it passes in the first second of time, in case he finds this to 
be one-fourth of 16 feet, the distance fallen through by the same body in 



TO STRUCTURE OF THE UNIVERSE. 

the same time, at the distance of 4000 miles from the earth's centre, the 
result would have confirmed the law which conjecture had assigned as 
the law of nature. Could he have mounted one unit higher, gaining an 
altitude of 8000 miles above the earth's surface, or three units from the 
centre, here repeating his experiment, in case the space passed through by 
the falling body is now one-ninth of 16 feet, it would yet farther confirm the 
truth of the conjectured law. Thus, could he have increased his altitude by 
one unit or radius of the earth after another, repeating his experiment as 
each new unit was added to his elevation, finding in every instance the law 
of diminution fulfilled by the falling body, all doubt as to the truth of the 
law would have been removed, and its foundation in nature would have 
justly flowed from such a series of experiments. 

Here, then, is precisely what must be accomplished to demonstrate the 
assumed law of gravitation. But since these altitudes of 4000 and 8000 
miles could not be reached, might not some change in the distance passed 
over by a heavy falling bod} T , be noticed and measured, if removed from 
a valley to the top of the highest mountain ? Alas ! the increased dis- 
tance from the centre of the earth, gained by ascending the loftiest 
mountain on its surface, is almost inappreciable, when compared with the 
entire distance, four thousand miles. Even if the mountain were ten 
miles high, the two elevations at which the experiment might then be 
performed, would be 4000 miles and 4010 miles, and the diminished veloc- 
ity would not be appreciable, even with the most delicate tests, much 
less could it be relied on to demonstrate the truth or falsehood of a great 
principle. Here, then, the mind was brought to a full stop ; and for a 
long time it seemed impossible that the philosopher should conquer the 
difficulties which rose up in his path, and defied his further advance. 
Finding it impossible to perform any satisfactory experiment on the 
earth's surface, the daring mind of Newton conceived the idea of employ- 
ing the moon itself as the falling body, and of testing the truth of his 
great theory by its fall towards the earth. But could he reach out his 
hand, grasp the revolving moon, stop it in its orbit, drop it to the earth, 
and measure its descent in the first second of time ? No — this was im- 
possible. The moon could not be arrested in its career; but is this neces- 
sary ? Is not the moon, in one sense, constantly falling towards the earth ? 
Newton asserted this to be true, and thus did he prove it. 

Stand upon the earth, and stretching outward into space 240,000 miles, 
there let the moon be located, poised and fixed in space, on a point of its 
present orbit. There let us suppose it to receive an impulse in a direction 
perpendicular to the line which joins it with the earth. By the first law 
of motion, being free to move, it will sweep off in a straight line, tangent 
to its present orbit, and will pass over a space in the first second of time, 
proportioned to the intensity of the impulse received. Mark that space, 
and bring the moon back to its primitive position. Now drop it towards 



LAWS OF MOTION AND GRAVITATION. ft 

the earth, and as it descends freely under the earth's attraction, mark the 
space through which it falls in the first second of time. This being 
known, bring back the moon once again to its starting-point. Now com- 
bine the impulsive force first given with that power which caused the 
moon, when left free to move, to fall to the earth. Let them both act at 
once : the impulse is given, the moon darts off in a straight line, but is 
instantly seized by the earth's attraction, which drags it from its rec- 
tilineal path, and the two contending forces, ever struggling, neither con- 
quering, exercise a divided empire over the moon ; onward she moves, 
obedient to the impulsive force, bent to her orbit by the action of the 
earth's attraction. Now the amount by which it is deflected in one 
second of time, from the straight line it would have pursued, is the 
amount precisely, by which it falls to the earth. 

If thus far I have been successful, what remains can readily be accom- 
plished. Newton easily computed, from the known velocity of the moon 
in its orbit, and from the radius of that orbit, the space through which 
the moon actually fell towards the earth in one second of time. He next 
computed the space through which a heavy body would fall towards the 
earth's surface, if removed from the earth to a distance equal to that of 
the moon. Now in case these two quantities should prove to be exactly 
equal, the truth of the demonstration would be complete ; the moon did 
fall through the space required by the assumed law, and in this event the 
law must be the law of nature. For seventeen long years did this incom- 
parable philosopher, rivaling the example of the immortal Kepler, toil on 
in this most difficult enterprise. He finally reaches the result ; the two 
quantities are found and compared, but alas ! the computed distance 
through which the moon must fall, in case the law of gravitation were 
true, differed from the observed distance through which it actually fell, by 
a sixth part of its value. Any less scrupulous, any less philosophic mind, 
would have been content with this near approximation, and would have 
announced the discovery to the world. Not so with Newton. Nothing 
short of the most rigorous accuracy could satisfy his conscientious regard 
for truth. His manuscripts are laid aside, and the pursuit for the present 
abandoned. 

Months roll by. Occasionally he returns to his computations, runs 
over the figures, hoping to detect some numerical error; but all is right, 
and he turns away. At length, while attending a meeting of the Royal 
Society in London, he learns that Picard had just closed a more accurate 
measurement of the diameter of the earth. This was one of the import- 
ant quantities which entered into his investigation. He returns home, — 
and with impatient curiosity spreads* before him his old computations — 
the new value of the earth's diameter is substituted — he dashes onward 
through the maze of figures — he sees them shaping their value towards 
the long sought result—the excitement was more than even his great 



7i STRUCTURE OF THE UNIVERSE. 

mind could bear — lie resigns to a friend — the work is completed, the 
results compared — they are exactly equal ! The victory is won, — he had 
seized the golden key which unlocks the mysteries of the universe, and 
he held it with a giant's grasp ! 

There never can come another such moment as the one we have de- 
scribed, in the history of any mortal. There are no such conquests re- 
maining to be made. Standing upon the giddy height he had gained, 
Newton's piercing gaze swept forward through coming centuries, and saw 
the stream of discovery flowing from his newly discovered law, slowly in- 
creasing, spreading on the right hand and on the left, growing broader, 
and deeper, and stronger, encircling in its flow planet after planet, sun 
after sun, system after system, until the universe of matter was encom- 
passed in its mighty movement. He could not live to accomplish but a 
small portion of this great work. — Rapidly did he extend his theory of 
gravitation to the planets and their satellites. Each accorded perfectly 
with the law, and rising as the inquiry was pursued, he at length an- 
nounced this grand prevailing law : 

Every particle of matter in the universe attracts every other particle of 
matter with a force or power directly proportioned to the quantity of matter 
in each, and decreasing as the squares of the distances ivhich separate the 
particles increase. 

Having reached this wonderful generalization, Newton now propound- 
ed this important inquiry. " To determine the nature of the curve which 
a body would describe in its revolution about a fixed centre, to which it 
was attracted by a force proportional to the mass of the attracting body, 
and decreasing with the distance according to the law of gravitation. '" 

His profound knowledge of the higher mathematics which he had 
greatly improved, gave to him astonishing facilities for the resolution of 
this great problem. He hoped and believed that when the expression 
should be reached, which would reveal the nature of the curve sought, 
that it would be the mathematical language descriptive of the properties 
of the ellipse. This was the curve in which Kepler had demonstrated 
that the planets revolved, and a confirmation of the law of gravitation 
required that the ellipse should be the curve described by the revolving 
body, on the conditions announced in the problem. 

There happens to be a remarkable class of curves, discovered by the 
Greek mathematicians, called the conic sections; thus named, because 
they can all be formed by cutting a cone in certain directions. The figure 
of a cone with a circle for its base, and converging to a point, is familiar 
to all. Cut this cone perpendicular to its axis, remove the part cut, and 
the line on the surface round the cone will be found to be a circle. Cut 
it again, oblique to the axis, then the line of division of the two parts will 
be an ellipse. Cut again so that the knife may pass downward parallel to 
the slope of the cone, and in this case your section is a parabola. Make 



LA WS OF MOTION AND ORA VITA TlON. 73 

a last cut parallel to the axis of the cone, and the curve now obtained is 
the hyperobla. 

When Newton reached the algebraic expression which, when interpreted, 
would reveal the properties of the curve sought and which he had hoped 
would prove to be the ellipse — he was surprised to find that it did not 
look familiar to his eye. He examined it closely — it was not the equation 
of the ellipse, and yet it resembled it in some particulars. What was his 
astonishment to find, on a complete examination, that the mathematical 
expression, which he had reached, expressing the nature of the curve 
described by the revolving body, was the general algebraic expression 
embracing all the conic sections. Here is a most wonderful revelation. Is 
it possible that under the law of gravitation, the heavenly bodies may 
revolve in any or either of these curves ? Observation responds to the 
inquiry. The planets were found to revolve in ellipses ; the satellites of 
Jupiter in circles ; and those strange, anomalous, outlawed bodies, the 
comets, whose motions hitherto had defied all investigation, take their 
place in the new and now perfect system, sweeping round the sun in 
parabolic and hyperbolic orbits. 

Thus were these four beautiful curves, having a common origin, possess- 
ed of certain common properties, yet diverse in character, mingling in 
close proximity, and gliding imperceptibly into each other, suddenly 
transferred to the heavens, to become the orbits of countless worlds. For 
nearly twenty centuries, they had been the objects of curious speculation 
to the mathematician ; henceforward they were to be given up to the 
hands of the astronomer, the powerful instrument of his future conquests 
among the planetary and cometary worlds. 

The three great laws of Kepler, to which he had risen with such 
incredible toil and labor, were now found to flow as simple consequences 
of the law of gravitation. It is impossible to convey the slightest idea, in 
discussions so devoid of mathematics, of the incredible change which had 
thus suddenly been wrought in the mode of investigation. I never have 
closed Newton's investigation, by which he deduces the nature of the 
curve, described by a body revolving around a fixed centre, under the 
law of gravitation, bearing with it consequences so simple yet so wonder- 
ful, without feelings of the most intense admiration. I can convey no 
adequate idea of the difference of the methods employed by Kepler and 
Newton, in reaching the three laws of planetary motion. I see Kepler in 
the condition of one on whom the fates have fixed the task of rolling a 
huge stone up some rugged mountain side, to its destined level, within a 
few feet of the summit. He toils on manfully, heaving and struggling, 
day and night, in storm and in darkness, never quitting his hold, lest he 
may lose what he has gained. If the ascent be too steep and rocky, he 
diverges to the right, then to the left, winding his heavy way zigzag up 
the mountain side.— -Years glide by — he grows gray in his toil, but he 



74 STRUCTURE OF THE UNIVERSE. 

never falters— onward and upward he still heaves the heavy weight — hi* 
goal is in sight, he renews his efforts, the last struggle is over — he ha& 
finished his task — the goal is won. 

Such was Kepler's method of reaching his laws. Now for Newton's. He 
/Stands, not at the base of the mountain, with its long, ascending rocky 
sides, but on the top. He starts his heavy stone, it rolls of itself over, 
slowly over, and once again, and falls quietly to its place. Let me not be 
misunderstood in this strange comparison, as detracting in the smallest 
degree from the just fame that is due to Kepler. But for his sublime 
discoveries, Newton could never have reached the mountain summit, on 
which he so proudly stood. Standing there, he never forgot by whose 
assistance he had reached the lofty point, and ever recognized, in the 
most public manner, his deep indebtedness to the immortal Kepler. 

A few words with reference to the rigorous application of Kepler's 
Jaws in nature, will close this discussion. The first law, announcing the 
revolution of the planets in elliptic orbits, was now made general, and 
recognized the revolution of the heavenly bodies in conic sections : the 
circle, ellipse, parabola and hyperbola. 

The second law, fixing the equality of the spaces passed in equal times, 
by the lines joining the planets to the sun as these were carried round in 
their elliptic orbits, now became applicable to all bodies revolving about a 
fixed centre, in any curve, and according to any law. 

The third law, recognizing the proportion between the squares of the 
periodic times and the cubes of the mean distances of the planets, was 
extended to the satellites, and to the comets ; modified slightly in the 
case of the larger planets, by taking into account their masses or quantities 
of matter. 

Here we close the era of research by observation. The mind has gained 
its last grand object. The era of physical astronomy dawns ; new and 
wonderful scenes open, and to the contemplatiop of thesp ^e shall soon 
invite your attention- 



LECTURE V. 

UNIVERSAL GRAVITATION APPLIED TO THE EXPLANATION OF THE 
PHENOMENA OF THE SOLAR SYSTEM. 

The progress of the mind, in its efforts to reach a satisfactory explana- 
tion of the movements of the heavenly bodies, previous to the discovery 
of universal gravitation, had been made independent of any guiding law. 
The mind had been feeling its way slowly and laboriously, guiding its 
direction by attentively watching the celestial phenomena, and relying for 
its success exclusively on the accuracy and number of its observations. 
Each discovery made was isolated, and although it prepared the way for 
the succeeding ones, it did not in any sense involve them as necessary con- 
sequences. By the discovery of the great law of universal gravitation, a 
perfect and entire revolution had been made in the science of astronomy. 
A new department was now added, which, previous to the knowledge of 
this law, could have no existence. In this branch of astronomy, the proc- 
ess of investigation being inverted, the mind descends from one great 
law to an examination of its consequences,. tracing these in their modified 
and diversified influences to their final limits. Observation is now em- 
ployed to verify discovery and not as the basis on which, and without 
which, discovery cannot be made. 

The era of physical astronomy is, therefore, the great era in the history 
of the science. It involves the resolution of the most wonderful problems 
— it calls into use the most refined and powerful mathematical analysis, 
and demands the application of the most ingenious and delicate instrument 
in seeking for the data by means of which its theory may be rendered 
practically applicable to the problems of nature. The mechanical philoso- 
pher in his closet may construct his imaginary system. In its centre he 
locates a sun, containing a certain mass of matter. — At any convenient 
distance from this sun he locates a planet, whose weight he assumes. To 
this planet he gives an impulse, whose intensity and direction are assumed. 
The moment these data are fixed, and the impulse given to the imaginary 
planet — no matter in what kind of an orbit it may dart away, whether 
circular, elliptical, parbolic or hyperbolic — the laws of motion and gravita- 
tion asserting their empire, the planet is followed by the mathematician, with 
a certainty and accuracy defying all escape. He assigns its orbit in the 
heavens — the velocity of its movement — the period of its revolution. In 



76 STRUCTURE OF TEE UHriVERSE. 

short, in a single line, lie writes out its history with perfect accuracy for a 
million years. 

If, now, to this simple system of a great central sun and one solitary 
planet, the physical astronomer add a third body, a moon, to the planet, 
he assumes its weight, the intensity and direction of the impulsive force 
starting it in its career, and now his system becomes more complex. Strike 
the sun out of existence, fix the planet, and the process of binding the 
satellite in mathematical fetters is precisely similar to that by which the 
movements of the planet were prescribed around the sun before the existence 
of the satellite. But now with these three bodies the train of investigation 
becomes more intricate and involved. While the planet alone circulated 
around the sun, such is the undeviating accuracy with which it will forever 
pursue its path around the sun, that if it were possible to hang up in space 
along its route golden rings whose diameter would just permit the flying 
planet to pass, millions of revolutions will never mark the slightest change. 
The rings once passed and then fixed, will mark forever the pathway of the 
solitary planet. But the moment a moon is given to this flying world, in 
that instant its motion is changed — it is swayed from its original fixed or- 
bit — it no longer passes through the golden rings, and although the physical 
astronomer may write out in his analytic symbols the future history of 
his planet and moon, these expressions are no longer marked with the 
simplicity which obtained in those which recorded the history of the single 
planet. While solitary, all changes were effected by the planet in one 
single revolution, and these were repeated in the same precise order in 
each successive revolution. Now, with the satellite added, there are 
changes introduced running through many revolutions, and requiring for 
their complete compensation vast periods of time. Indeed, the inquir} r 
arises, whether this system of a central sun, with a planet and its satellite 
revolving about it, can be so constituted that the changes which the 
planet and its moon mutually produce on each other's movements may 
not go on constantly accumulating in the same direction until all features 
of the original orbits of both may be destroyed, both worlds being finally 
precipitated on the sun, or driven farther and farther from this luminary, 
until they are lost in infinite space. This inquiry, in a more extended 
form, will be examined hereafter. We proceed to build up our imaginary 
system. Thus far we have regarded our planet and its satellite as mere 
material heavy points. In case we give to them magnitude and rotation 
on an axis, the velocity of rotation will determine the figure of the 
planet and of its satellite. These figures will deviate from the exact 
spherical form, and this change of figure will sensibly affect the stability 
of the axis of rotation, and will introduce a series of subordinate move- 
ments, each of which must become the subject of research ; and to write 
out the future history of the system these minute and concealed changes 
must likewise receive their mathematical expression. 



UNIVERSAL GRAVITATION. ft 

Having thus thoroughly mastered all the phenomena of this system of 
three bodies, the astronomer now adds another planet, whose mass is as- 
sumed, together with the direction and intensity of its primitive impulse. 
Its orbit is now computed, subject to the greatly predominant influence 
of the sun, but sensibly affected by the quantity of matter in the old planet 
and its satellite, which prevents it from forming a fixed and unchangeable 
orbit in space. Again he is obliged to return to an examination of his 
first planet and its moon, for these again break away from their previous 
routes, and in consequence of the action of the second planet, assume new 
orbits, and are subjected to periodical fluctuations, which demand critical 
examination, and without a knowledge of which no truthful history of the 
planetary system can be written. To the second planet let us now add 
several satellites, each of which has its mass assigned, and the direction 
and intensity of the impulsive force by which they are projected in their 
orbits. Here, then, is a subordinate system demanding a complete ex- 
amination. The satellites mutually affect each other's motions, and each 
is subjected to the influence of the primitive planet and its moon. Again 
does the physical astronomer review his entire investigation. The ad- 
dition of these satellites to his second planet has introduced changes in 
all the previous bodies of the system, which must now be computed, to 
keep up with the growing complexity. This task is at last accomplished. 
All the changes are accurately represented. Analysis has mastered the 
system, and the history of its changes are written out for hundreds and 
thousands of years. 

A third planet, with its satellite, is now added. This new subordinate 
system is discussed, and its operation on all the previous planets and 
satellites computed, and after incredible pains, the astronomer once more 
masters the entire group, and follows them all with unerring precision, 
through cycles of changes comprehending thousands or even millions of 
years. 

Thus does the difficulty of grasping the system increase in a high ratio 
by the addition of every new planet and satellite, till finally the last one 
is placed in its orbit, and the system is complete, so far as planets and 
satellites are concerned. Through this complicated system now cause 
thousands of comets to move in eccentric orbits, coming in from every 
quarter of the heavens, plunging downwards towards the sun, sweeping 
with incredible velocity around this central luminary, and receding into 
space to vast distances, either to be lost forever, or to return after long 
periods to revisit our system. These wandering bodies must be traced 
and tracked, their orbits fixed, their periods determined, their influence 
on the planets and satellites, and that exerted by these on the comets, 
must be computed and determined ; then, and not till then, does the 
physical astronomer reach to a full knowledge of this now almost infinitely 
complex system. 



78 STRUCTURE OF THE UNIVERSE. 

In this imaginary problem it will be observed that certain quantitie? 
were invariably assumed before the discussion could proceed. The mass 
of the sun — the mass of each planet and satellite — the intensity and 
direction of the primitive impulse given to each planet and satellite — 
these quantities are supposed to be known. If, now, the astronomer has 
actually accomplished the resolution of the^imaginary problem, and has 
obtained analytic expressions which write out and reveal the future 
history of his assumed planets and satellites, as they revolve around his 
assumed sun, if in these expressions he should substitute the actual 
quantities which exist in the solar system for those assumed, his expres- 
sions would then give the history of the solar system for coming ages, and 
by reverse action would reveal its past history with equal certainty. 

Before we can, therefore, bring the power of analysis to bear on the 
resolution of the grand problem of nature, we must interrogate the 
heavens, and obtain the absolute weight of our sun, of each planet, and 
of every satellite. Next we require the intensity and direction of the 
impulsive force which projected each planet and satellite in its orbit, and 
which would have fixed forever the magnitude and position of that orbit, 
in case no disturbing causes had operated to modify the action of the 
primitive impulse. 

Having thus attempted to exhibit, at a single view, the general out- 
lines of the great problem of the solar system, we propose now to return 
to the examination of a system composed of three bodies ; and to fix our 
ideas, we assume the sun, earth, and moon. In case the earth existed 
alone, the elliptic orbit described in its first revolution around the sun 
would remain unchanged forever, and having pursued it, and marked its 
changes of velocity in the different parts of its orbit for a single revolu- 
tion, this would be repeated for millions of years. But let us now give 
to the earth its satellite, the moon, and setting out from its perihelion, or 
nearest distance from the sun, let us endeavor to follow these two bodies 
as they sweep together through space, and mark particularly the effect 
produced on the moon's orbit by the disturbing influence of the sun. 
To give to the problem greater simplicity, let us conceive the plane of the 
moon's orbit to coincide with the earth's. The law of gravitation which 
gives to every attracting body a power over the attracted one, gravity in- 
creasing as the distance decreases, it will be perceived that when the 
earth and moon are nearest to the sun, whatever influence the sun pos- 
sesses to embarrass or disturb the motions of the moon about the earth, 
will here be exercised with the greatest effect. But since the sun is ex- 
terior to the moon's orbit, its tendency will be to draw the moon away 
from the earth, and cause her to describe around her primary a larger 
orbit, in a longer period of revolution than would have been employed in 
case no sun existed, and the moon was given Up to the fekcl-usive control 
of the earth, 



UNIVERSAL GRAVITATION. 79 

Starting the planet on its annual journey, as it recedes from the sun in 
passing from its nearest to its most remote distance, or from perihelion to 
aphelion, the moon is gradually removed from the disturbing influence of 
the sun ; it is subjected more exclusively to the earth's attraction ; its dis- 
tance from the east grows less, and the periodic time becomes shorter. 
These changes continue in the same order until the earth reaches its 
aphelion. There the moon's orbit is a minimum, and its motion is 
swiftest. In passing from the aphelion to the perihelion, the earth is con- 
stantly approaching the sun, and as the sun's influence on the moon in- 
creases as its distance diminishes, its orbit will now expand by slow 
degrees, and the periodic time will diminish until on reaching the peri- 
helion, in case the figure of the earth's orbit remains unchanged, the 
moon's periodic time will be restored to its primitive value, and all the 
effects resulting from the elliptic figure of the earth's orbit will have 
been entirely effaced. 

Thus far we have directed our attention exclusively to the changes in 
the distance of the moon and its periodic time. But the moon's orbit is 
elliptical, as well as the earth's, and it is manifest that the sun's influence 
will operate to change not only the magnitude of this orbit, but will in like 
manner produce a change in the position of the moon's perigee, or nearest 
point of distance from the earth. If the earth were stationary, and the 
moon revolved around it, passing between it and the sun, and then com- 
ing around so as to be beyond the earth with respect to this luminary, 
although the moon's orbit would be sensibly affected by the sun's attrac- 
tion, yet this having exerted itself during one revolution of the moon, all 
its effects would be repeated in the same order during the next revolu- 
tion, and the relative positions of the sun and earth remaining the same, 
the moon would come finally to have- a fixed orbit, and its principal lines 
or axes would never change. But this is not the case of nature. — The 
earth swiftly turning in its orbit, and bearing with it its revolving satellite, 
by the time the moon has completed a revolution, the sun and earth have 
entirely changed their relative positions, and the moon cannot reach its 
perigee, or nearest distance from the earth, at the same point as in the 
preceding revolution. 

By an attentive examination of this problem, it is found that the tend- 
ency is to cause the moon to reach its perigee earlier than it would do if 
not disturbed, and in this way the perigee of a fixed orbit appears to ad- 
vance to meet the coming moon, and in the end to continue advancing 
until it actually revolves entirely round in a period which observation de- 
termines to be about nine years. 

it is not my intention to enter into a detailed examination of all the 
effects resulting from the sun's disturbing power on the moon's motions ; 
neither shall I attempt to exhibit all the effects produced by the moon on 
the earth. — This would require a train of investigation too elaborate and 



80 STRUCTURE OF THE UNIVERSE. 

intricate to comport with my present purposes. My object is simply to 
show that changes must arise from the mutual and reciprocal action of 
these three bodies, which the theory of gravitation must explain, and the 
telescope point out, before it be possible to obtain a perfect knowledge of 
these bodies. 

The exact estimation of these changes can never be made until we shall 
have learned the relative masses of matter contained in the sun, earth, and 
moon. In other language, we must know how many moons it would re- 
quire to weigh as much as the earth, and how many earths would lorm a 
weight equal to that of the sun. 

But is it possible that man, situated upon our planet, 237,000 miles from 
the moon, and 95,000,000 of miles from the sun, can actually weigh these 
worlds against each other, and determine their relative masses of matter ? 
Even this has been accomplished, and I shall now proceed to explain how 
the earth may be weighed against the sun. Dropping a heavy body at 
the earth's surface, the velocity impressed on it in the first second of time 
will measure the weight of the earth in one sense. If it were possible to 
take the same body to the sun, drop it, and measure the velocity acquired 
by the falling body in the first second of time, the relative distances 
passed through at the sun and at the earth by the same body in the same 
time, would show exactly the relative weight of the sun and earth, for 
their capacity to communicate velocity are exactly proportioned to their 
masses. Now, although this experiment cannot be performed in the exact 
terms announced, yet as we have already shown, the moon is constantly 
dropping towards the earth, and the earth is as constantly dropping to- 
wards the sun. Now in case we measure the amount by which the moon 
is deflected from a straight line in one second of time, this measures the 
intensity of the earth's power. But the amount by which the earth is de- 
flected from a right line by the central power of the sun in one second, is 
easily measured from a knowledge of its period and the magnitude of its 
orbit. Executing these calculations, it is found that the sun's effect on 
the earth is rather more than twice as great as the earth's effect on the 
moon, and in case these effects were produced at equal distances, then 
would the sun be shown to contain rather more than twice as much matter 
as is found in the earth. But the sun produces its effect at a distance 
400 times greater than that at which the earth acts on the moon ; hence, 
as the force diminishes as the square of the distance increases, a sun act- 
ing at twice the distance at which the earth acts, must be four times 
heavier to produce an equal effect ; at three times the distance, it must 
be nine times heavier, and at four times the distance, sixteen times heavier ; 
— at 400 times the distance, 160,000 times heavier than the earth. Thus 
do we find that in case the sun's action on the earth were exactly equal 
to the earth's action on the moon, in consequence of the great distance 
at which it operates, its weight would be equal to that of 160,000 earths. 



UNIVERSAL GRAVITATION. 81 

But its actual effect is rather more than double that of the earth on the 
moon, and hence we find it contains rather more than double 160,000 
earths, or exactly 354,936 times the quantity of matter contained in the 
earth. 

This enormous mass of the sun is confirmed by an examination of its 
actual dimensions. An object with an apparent diameter equal to that of 
the sun and at a distance of 95,000,000 of miles, must have a real diameter 
of 883,000 miles, a quantity so great that if the sun's centre were placed 
at the earth's centre, its vast circumference would give ample room for 
the moon to circulate within its surface, leaving as great a space between 
the moon's orbit and the sun's surface as now exists between the moon and 
earth. 

It is this immense magnitude of the sun, when compared with the planets 
and their satellites, which renders the orbits of the planets comparatively 
unalterable. It is true that these bodies mutually affect each other, but 
these effects are comparatively slight, and astronomers regard them as 
perturbations, or mere disturbances of the original elliptic motion. Hence 
we find the magnitude and position of the earth's elliptic orbit remain 
without any very sensible variation for two or three revolutions ; but the 
slight disturbance experienced at each revolution, constantly accumulating 
in the same direction in a long series of years, occasions changes that can- 
not be lost sight of, and which, by a reflex influence, become in some in- 
stances exceedingly important in their practical applications. 

As it will be impossible to treat fully the complex subject of perturbation, 
I will call your attention to a few points about which cluster peculiar in- 
terests, in consequence of their great difficulty, and the almost infinite 
reach of analysis displayed in their successful examination. 

I have already explained how it is that the disturbing influence of the 
sun occasions a constant fluctuation in the periodic time of the moon, ac- 
celerating it as the earth moves from perihelion to aphelion, and again re- 
tarding it from aphelion to perihelion. If, now, we take a large number 
of revolutions of the moon, say a thousand, add them all up, and divide 
by one thousand, we obtain a mean period of revolution, which, in case the 
earth's orbit remains invariable will never change, but will be constantly the 
same for thousands of years. By such an examination during the last cent- 
ury, the mean motion of the moon was obtained with great precision. But 
on a comparison of eclipses recorded by the Babylonians with each other, 
it was discovered that the moon in those early ages required a longer time 
to perform her mean revolution than in modern times. Alike comparison 
of the Babylonian eclipses with those recorded in the middle ages by the 
Arabian astronomers, confirmed this wonderful discovery, which was yet 
farther substantiated by comparing the Arabian eclipses with those ob- 
served in modern times. It thus became manifest that, to all appearance 
at least, the moon's mean motion was growing swifter and swifter from 

6 



82 STRUCTURE OF THE UNIVERSE. 

century to century ; that it was approaching closer and still closer to the 
earth, and if no limit to this change was ever to be fixed, sooner or later 
the final catastrophe must come, and the moon be precipitated on the body 
of the earth, and the system be destroyed. 

An effort was made to account for this acceleration of the moon, on the 
theory of gravitation ; but for along time there seemed to be no possibility 
of rendering a satisfactory explanation of the phenomena, far less of pre- 
scribing the limits which should circumscribe the changes. Some, to 
escape from the difficulty, rejected entirely the ancient eclipses, and boldly 
cut the knot, by pronouncing the acceleration as impossible, and without 
any foundation in fact. — Others admitted the fact, but finding it impossi- 
ble to account for it on the hypothesis of gravitation, conceived the idea 
that the moon was moving in some ethereal fluid capable of resisting its 
motion, and producing a diminution in its periodic time of revolution. That 
acceleration should be the effect of resistance, may seem to some very 
strange, but a little reflection will render the subject clear. In case the 
moon's orbitual motion is resisted, then the centrifugal force, which 
depends on the velocity, becomes diminished, and the central power of the 
earth draws the moon closer to itself, decreases the magnitude of its orbit, 
and in like manner reduces the time of accomplishing one revolution about 
the earth. 

Finding no better solution of the mystery, and being obliged to acknowl- 
edge the fact that the mean motion of the moon was becoming swifter and 
swifter, from the action of a resisting medium, there was no escape from 
the final consequences ; and it was by some believed that the elements of 
decay existed, that the doom of the sj^stem was fixed, and although thou- 
sands, possibly millions, of years might roll away before the fatal day, yet 
it must come, slowly, but surely as the march of time. Such was the con- 
dition of the problem when Laplace gave the powers of his giant intellect 
to the resolution of this mysterious subject. The consequences involved 
gave to it an unspeakable interest, and the world waited with keen anxiety 
to learn the result of the investigations of this great geometer. Long and 
difficult was the struggle — slow and laborious the task of devising and 
tracing out the secret causes of this inscrutable phenomenon. The planets 
are weighed and poised against the earth, their effects computed on its 
orbit, the final result of these effects determined, and the reflex influence 
on the moon's motion computed with the most extraordinary precision. 
Under the searching examination of Laplace's potent analysis, nature is 
conquered, the mystery is resolved, the law of gravitation is vindicated — ■ 
the system is stable, and shall endure through periods whose limits God 
alone, and not man, shall prescribe. 

Follow me in a simple explanation of this most remarkable discovery. 
It has already been stated, that in case the earth's orbit could remain 
mashanged, that the mean period of the moon, as derived from a thousand 



UmVEESAL GBAVITATION. 83 

of its revolutions, would be constant, and would endure without the 
slightest change for millions of years. But this permanency of the earth's 
orbit does not exists. — Laplace discovered that under the joint action of 
all the planets, the figure of the earth's orbit was slowly changing ; that 
while its longer axis remained invariable, that its shape was gradually be- 
coming more and more nearly circular. At the end of a vast period, its 
ellipticity would be destroyed, and the earth would sweep around the sun 
in an orbit precisely circular. Attaining this limit, a reversed action 
commences — the elliptic form is resumed by slow degrees — the eccentric- 
ity increases from age to age — until, at the end of millions of years, a 
second limit is reached. The motion is again reversed — the orbit again 
opens out, approaches its circular form, and thus vibrates backwards and 
forwards in millions of years, like some mighty pendulum beating the 
slowly ebbing seconds of eternity ! 

But do you demand how this change in the figure of the earth's orbit 
can effect the moon's mean motion ? The explanation is easy. Were it 
possible to seize the earth and hurl it to an infinite distance from the sun, 
its satellite, now released from the disturbing influence of this great 
central mass, would yield itself up implicitly to the earth's control. It 
would be drawn closer to its centre of motion, and its orbit being thus 
diminished, its periodic time would be shorter, or its motion would be 
accelerated or made swifter than it now is. This is an exaggerated hy- 
pothesis, to render more clear the effect produced by removing the earth 
farther from the sun. Now the change from the elliptical to the circular 
form, which has been progressing for thousands of years, in the earth's 
orbit, is, so far as it goes, carrying the earth at each revolution a little 
farther from the sun, releasing in this way the moon, by slow degrees, 
from the disturbing influence of that body ; giving to the earth a more 
exclusive control over the movements of its satellite, and thus increasing 
the velocity of the moon in its orbit from age to age. But will this 
acceleration ever reach a limit ? Never, until the earth's orbit becomes 
an exact circle, at the end of millions of years. Then, indeed, does the 
process change. At every succeeding revolution of the earth in its orbit, 
its ellipticity returns — its distance from the sun diminishes — the moon is 
again subjected more and more to the action of the sun, is drawn farther 
and farther from the earth, and its periodic time slowly increases. Thus 
is acceleration changed into retardation, and at the end of one of these 
mighty cycles, consisting of millions of years, an exact compensation is 
effected, and the moon's motion having gone through all its changes, 
once more resumes its original value. 

I can never contemplate this wonderful revolution without feelings of 
profound admiration. Such is the extreme slowness of this change in the 
moon's mean motion, that in the period of three thousand years she has 
got only four of her diameters in advance of the position she would have 



84 STRUCTURE OF THE UNIVERSE. 

occupied in case no change whatever had been going on. Here, then, is 
a cycle of changes extending backward to its least limit millions of years, 
and extending forward to its greatest limit tens of millions of years, 
detected and measured by man, the existence of whose race on our globe 
has scarcely been an infinitesimal portion of the vast period required for 
the full accomplishment of this entire series of changes. 

May it not, then, be truly said, that man is in some sense immortal, 
even here on earth. What is time to him, who embraces changes in 
swiftly revolving worlds, requiring countless ages for their completion, 
within the limits, of an expression so condensed that it may be written in 
a single line ? Does he not live in the past and in the future, as abso- 
lutely as in the present ? Indeed, the present is nothing — it is the past 
and future which make up existence. 

In the example of the moon's acceleration just explained, we must not 
fail to notice ,a most remarkable fact. It is this : — The slow change in the 
figure of the earth's orbit, occasioned by the joint action of all the planets, 
and upon which depends the acceleration of the moon's mean motion, is 
so disguised, that but for its reflex influence on the moon, the probability 
is it would have escaped detection for thousands of years. The direct 
effect is almost insensible, but being indirectly propagated to the moon, 
it is displayed in a greatly exaggerated manner — is in this way detected, 
and finally, after incredible pains, traced to its origin, and demonstrates 
in the most beautiful manner the prevalence of the great law of universal 
gravitation. 

Since the general adoption of this law, the human mind has been, in 
not a few instances, disposed to abandon its universality, and seek for a 
solution of some intricate problem, by which it was perplexed, in some 
change or modification of the law ; but in no instance has the effort to fly 
from the law been successful. No matter how long and intricate the ex- 
amination, how far the mind might be carried from this great law, in the 
end it must come back and acknowledge its universal empire over our 
entire system. 

It has already been remarked, that one of the effects of the sun's 
disturbing influence exerted on the moon, was to occasion a change in the 
position of its perigee, causing it to complete an entire revolution in the 
heavens in about nine years. The theory of gravitation gave a very 
satisfactory account of this phenomenon generally ; but when Sir Isaac 
Newton undertook the theoretic computation of the rapidity with which 
the moon's perigee should move, he found, to his astonishment, that no 
more than one half of the observed motion of the perigee was obtained 
from theory. In other language, in case the law of gravitation be true, 
Newton found that the moon's perigee ought to require eighteen years to 
perform its revolution in the heavens, while observation showed that the 
revolution was actually performed in one half of this period. This great 



tmiVEnSAL GRAVITAT10K. 85 

philosopher exhausted all his skill and power in the vain effort to over- 
come this difficulty. He died, leaving the problem unresolved, bequeath- 
ing it to his successors, as a research worthy of their utmost efforts. 

Astronomers did not fail to recognize the high claims of this investiga- 
tion. Gravitation was once more endangered. The most elaborate com- 
putations were made, and the results obtained by Newton were so invari- 
ably verified by each successive computer, that it seemed utterly impos- 
sible to avoid the conclusion ; — they were absolutely accurate, and that 
the theory of gravitation must be modified in its application to this pe- 
culiar phenomenon. At length the problem was taken up by the distin- 
guished astronomer Clairaut. After repeating, in the most accurate 
manner, the extensive computations of his predecessors, reaching invari- 
ably the same results, he finally abandoned the law of gravitation in 
despair, pronounced it incapable of explaining the phenomenon, and under- 
took to frame a theory which should be in accordance with the facts. 

This startling declaration of Clairaut excited the greatest interest. 
An abandonment of the theory of gravitation was nothing less than 
returning once more to the original chaos which had reigned in the 
planetary worlds, and of commencing again the resolution of the great 
problem which it had long been hoped was entirely within the grasp of 
the human intellect. In this dilemma, when the physical astronomer had 
abandoned the law r of gravitation in despair, and the legitimate defenders 
of the theory were mute, an advocate arose where one was least to be ex- 
pected. Buffon, the eminent naturalist and metaphysician, boldly 
attacked the new theory of Clairaut, pronounced it impossible, and defended 
the law of gravitation by a train of general reasoning, which the astrono- 
mer felt almost disposed to treat with ridicule. What should a natu- 
ralist know of such matters ? was rather contemptuously asked by the 
astronomer. It is true he knew but little, yet his attack on Clairaut 
had the effect to induce the now irritated astronomer to return to his 
computations, with a view to overwhelm his adversary. He now deter- 
mined to rest satisfied with nothing short of absolute perfection. — A 
certain series which had been reached by every computer, and the value 
of whose terms had been regarded as decreasing by a certain law, until 
they finally became inappreciable, from their extreme minuteness, and 
therefore might, without sensible error, be rejected, was found, on a more 
careful examination, to undergo a most remarkable change in its character. 
It was true that the value of its terms did decrease till they became 
exceedingly small ; but so far from becoming absolutely nothing, on 
reaching a certain value, the decrease became changed into increase — the 
sum of the series expre««ing the velocity of the moon's perigee was in 
this way actually doubled, and Clairaut found, to his inexpressible as- 
tonishment, that the investigation which had been commenced with the 
intention of forever destroying the universality of the law of gravitation, 



86 8TBUCTUBE OF TBE UNIVERSE. 

resulted in his own defeat, and in the perfect and triumphant establish- 
ment of this great law. 

Thus far, in our examinations of the moon and earth, we have regarded 
their orbits as lying in the same plane, an hypothesis which greatly sim- 
plifies the complexity of their motions. This, however, is not the case of 
nature. The moon revolves in an orbit whose plane is inclined under an 
angle of about four degrees to the plane of the ecliptic. During half of 
its journey, it lies above the plane of the earth's orbit, while the remain- 
ing part of its route is performed below the ecliptic. Thus does the 
moon, at each revolution, pass through the ecliptic at two points, called 
the nodes, which points, being joined by a straight line, gives us the inter- 
section of the plane of the moon's orbit with that of the earth. This line 
of intersection, called the line of the nodes, but for the disturbing influ- 
ence of external causes, would remain fixed in the heavens. But we 
know it to be constantly fluctuating, and in the end performing an entire 
revolution. The exact amount of this change has been made the subject 
of accurate examination, and the law of its movement has been found 
to result precisely from the law of gravitation. Not only is the line of 
intersection of the plane of the moon's orbit with that of the earth con- 
stantly changing, but theory, as well as observation, has ascertained that 
a series of changes are equally progressing in the angles of inclination of 
these two planes. The limits are narrow, but the oscillations are unceas- 
ing, complicating more and more the relative motions of these two 
remarkable bodies. 

In the physical examination of the revolution of the planetary orbs by 
the application of the law of gravitation, the general features of the in- 
vestigation are greatly simplified by the fact that the planets and satellites 
may be regarded as spherical bodies, and may in general be treated as 
though their entire mass were condensed into a material heavy point situ- 
ated at their centre. While this statement is true in its broader applica- 
tion to the theory of planetary perturbations, or even in the theory of 
the sun's action on the planets, especially the more distant ones, it is 
by no means to be admitted, when we come to a critical examination of 
the figures of the planets^ and the influence exerted by these figures on 
their near satellites. 

In case the earth had been created an exact sphere, and had been pro- 
jected in its orbit without any rotation on an axis, then would its globular 
figure have remained without sensible change. But as it revolves swiftly 
on its axis, the laws of motion and gravitation come in to modify the figure 
of the earth, and to change it from an exact spherical figure to one which 
is flattened at the poles and protuberant at the equator. Newton's sagacity 
detected this result as a necessary consequence of the action of gravita- 
tion, and he actually computed the figure of the earth from theory, long 
before any observation or measurement had created a suspicion that its 



UNIVERSAL GRAVITATION. 87 

{■> m was other than spherical. The truly wonderful train of conse- 
quences flowing from the spheroidal form of the earth gives to this 
subject a high interest, and demands as close an examination of its prin- 
cipal features as the nature of our investigations will permit. 

Give to the earth, then, an exactly spherical form, and a diameter of 
8000 miles, with a rotation on an axis once in twenty-four hours, and let 
us critically examine the consequences. A particle of matter situated on 
the equator is 4,000 miles from the earth's axis, and since it passes over 
the circumference of a circle whose radius is 4,000 miles, it will move 
with a velocity of about one thousand miles an hour. As we recede 
from the equator towards the poles, either north or south, the particles 
revolve at the extremities of radii constantly growing shorter and shorter, 
until finally at the exact pole there is no motion whatever. But in 
every revolving body, a centrifugal force is generated — a tendency or 
disposition to fly from the axis of rotation in a plane perpendicular to 
this axis. 

Such is the power of this centrifugal force, that if it were possible to 
make the earth rotate seventeen times in twenty-four, instead of once, 
bodies at the equator would be lifted up by the centrifugal force, and the 
attraction of gravitation would be counterpoised, if not absolutely over- 
come. The force of gravity exerts its power in directions passing nearly 
through the centre of the earth, while the centrifugal force is always ex- 
erted in a direction perpendicular to the axis of rotation. The conse- 
quence is manifest, that these two forces cannot counterpoise each other, 
except in their action on particles situated on the equator of the revolving 
bod} r . Let us consider the condition of a particle situated anywhere be- 
tween the equator and the pole, and free to move under the joint action 
of these two forces. 

In order that such a particle may be held in equilibrium, the two forces 
must act on the same straight line, and in opposite directions. This is 
not the case in question, for gravity draws the particle to the centre of 
the earth, while the centrifugal force urges it from the axis in a plane 
perpendicular to that axis. The direction of these two forces is inclined 
under an angle which is nothing at the equator, and increases from the 
equator to the poles. But the effect produced by the centrifugal force 
may always be obtained by the joint action of two forces, the one directed 
to the centre of the earth, the other tangent to the earth's surface, Sub- 
stituting these two forces for the centrifugal force, we perceive that the 
partial force directed towards the earth's centre is destroyed by gravita- 
tion, while the tangential force exerts its full power to move the particle 
towards the equator of the earth. 

This being understood, it is manifest that as particles are coming con- 
stantly from both poles towards the equator, that a change of figure in the 
earth must be effected. It becomes protuberant at the equator, and is 
flattened at the poles. 



88 STRUCTURE OF THE UNIVERSE. 

The question now arises, whether there be any limit to this change of 
figure. In case the velocity of rotation continues undiminished, is there 
not reason to fear that the earth will grow more and more protuberant at 
the equator, heaping up the matter higher and higher, till the figure of 
the earth be destroyed, and its surface rendered uninhabitable ? Theory 
has answered this important question ; and it has been fully demonstrated 
that the figure of the earth cannot pass a limit, which it has even now 
actually attained, and its present form will not change, from the action of 
the centrifugal force, in millions of years. A condition of equilibrium has 
been attained, and all further change is at an end. Indeed, if we examine 
carefully the subject, we may readily perceive, from the nature of the 
forces, and the conditions of the problem, that such a result might have 
been anticipated. As the earth grows more protuberant, changing from 
the spherical form, the particles must be heaved up the side of this ele- 
vated ridge which belts the earth around the equatorial regions, and fin- 
ally the resistance they meet from the elevation they are obliged to over- 
come, is quite equal to the moving force, and the two destroy each other. 
This point attained, equilibrium ensues, and further change becomes im- 
possible. 

Such is the beautiful order of nature, such the admirable arrangement 
for stability and perpetuity, everywhere manifested, that the thought 
constantly comes to the mind that divine wisdom alone could have framed 
so admirable a system. 

But the question may here arise, is this a mere theoretic result? Has 
observation confirmed the theoretic figure? I answer that observations, 
the most numerous and diversified, have all united their harmonious testi- 
mony to the truth of these beautiful results. In executing exact meas- 
ures of the degrees of a meridian passing through the poles round the 
earth, the length of the degree is found to increase from the equator 
towards the poles, showing that the curvature is more flattened as we re- 
cede from the equator. But a more delicate proof is found in the vibra- 
tions of the pendulum. A pendulum of a given length will vibrate with a 
velocity precisely proportioned to the intensity of the force of gravity 
which operates on it. But the intensity of gravity decreases as the square 
of the distance from the centre increases, so that it is manifest that the force 
of gravity is less at the equator than at the poles, in case the surface at 
the equator is farther from the centre than at the poles, which is the fact 
asserted by theory i 

This being understood, we are prepared to determine the exact figure 
of the earth, by transporting a pendulum of given length from the equator 
to different latitudes north and south. — The number of vibrations in one 
hour being accurately counted at the equator, as we recede north or south, 
will determine with certainty whether we are approaching to, or going 
farther from the earth's centre. These experiments have actually been 



VmVESSAL GRAVITATION. 89 

performed, and with the most satisfactory results. The number of vibra- 
tions in an hour increases the farther we go north or south, and in a ratio 
giving the strongest confirmation to the truth of the earth's figure derived 
from the theoretic investigations — each combining to show that the polar 
diameter of the earth is but 7,898 miles, while the equatorial diameter is 
7,924 miles, producing a sort of ridge or belt around the equatorial regions, 
rising about thirteen miles above the general spherical surface described 
about the polar axis as a diameter. 

More than two thousand years have passed away since a discovery was 
made, showing that the sun's path among the fixed stars was slowly 
changing. — The point at which it crossed the equatorial line, and which 
for ages had been regarded as fixed, was finally detected to have a slow 
retrograde motion, producing the precession of the equinoxes. The fact 
was received but, no depth of penetration, no stretch of intellectual vigor 
could divine the cause of this inexplicable change. Another fact was re- 
vealed about the same time. It was found by attentive examination, that 
the north pole of the heavens, the point in which the prolongation of the 
earth's axis pierces the celestial sphere, was actually changing, by slow de- 
grees, its place among the fixed stars. The bright star which, in former 
ages, had marked the place of the pole, and whose circle of diurnal revolu- 
tion was scarcely to be perceived from its smallness, as centuries slowly 
glided by, was increasing its distance from the pole, gradually describing 
round it a circle of greater radius. An attentive examination of the stars 
near the pole soon demonstrated the fact, that it was an actual motion of 
the pole, and not of the stars in its neighborhood. 

Now, incredible as this statement may appear, modern science has traced 
these phenomena, the revolution of the equinoctial point, and the move- 
ment of the north pole of the heavens, to a common origin, and has de- 
monstrated, in the clearest manner, that they are both consequences of the 
spheroidal figure of the earth, which we have just examined. It is not 
my design to enter into an elaborate investigation of this wonderful sub- 
ject, but, in accordance with the plan already announced, I cannot leave 
you with a mere announcement of a truth so startling, without some effort 
to explain how this may be. The subject is difficult, but favored by your 
close attention, I do not despair of rendering it approximately intelligible. 

Let us conceive the earth's axis to be a solid bar of iron driven through 
the centre of the earth, coming out at the poles, and extending indefinitely 
towards the sphere of the fixed stars. Now turn this axis up until it stands 
perpendicular to the plane of the orbit in which the earth revolves 
round the sun. Then do the equator and ecliptic exactly coincide, and 
the fixed stars are at a distance nearly infinite, the point in which 
the earth's. axis prolonged pierces the heavens will appear stationary, 
so far as the revolution of the earth in its orbit is concerned. Now if this 
iron axle could be grasped by some giant hand, and drawn away from its 



GO STRUCTURE OF THE UNIVERSE. 

upright or perpendicular position, the solid earth would turn with it, and 
the equator, ceasing to coincide with the ecliptic or plane of the earth's 
orbit, comes to be inclined to it, under an angle precisely equal to the 
angle through which the axis has been inclined. It is thus seen that no 
change can be wrought on the position of the axis, that does not involve a 
corresponding change in the whole earth, and especially in the plane of 
the equator, which must ever remain perpendicular to the axis in all its 
positions. 

The reverse of this proposition is equally manifest. If the solid earth 
be seized at the equator, and be turned up or down, the axis will participate 
in this movement, and its changes will exhibit itself in the changed posi- 
tion of the point in which it meets the celestial sphere. One step more, 
and the difficulty is surmounted. — Conceive a flat wheel of wood floating 
on still water. Through its centre pass an axle which stands perpendicular 
to the surface of the wheel and water. So long as the wheel floats level, 
the axle stands erect, but in case the north half of the wheel is tilted down 
under the water, the south half at the same time rising out of the water, 
the axis will tilt towards the north. Bring the wheel again to its level 
position. Now plunge the eastern portion of the wheel below the surface. 
— The axis now is tilted towards the east. — The experiment is simple, and 
shows that, in case the successive portions of the wheel be submerged, the 
axis will always be tilted towards the point which goes under first. To 
reverse the experiment : in case we take hold of the axle and turn it east 
it sinks the eastern half of the wheel below the surface of the water, while 
the western half is raised out of it, and then in case we make the upper 
extremity of the axis follow round the circumference of a circle whose sur- 
face is parallel to that of the water, and whose centre is exactly above the 
centre of the wheel, it will be seen that, as the axle moves round, successive 
portions of the wheel are sumerged, until finally the water line will have 
divided the wheel into all its successive halves, and will have successively 
coincided with every possible diameter of the wheel. 

Now for the application. The level surface of the water is the level plane 
of the earth's orbit, the wheel is the earth's equator, and the axle is the 
earth's axis of rotation. One-half of the equator is constantly submerged 
below the plane of the ecliptic — the other half rises above it. But the 
water line, or the intersection of these two planes, the equinoctial line, can- 
not remain fixed in the same line. A power does seize the equator and 
plunge successive halves of it beneath the plane of the ecliptic, changing 
perpetually the water line, until finally each half in succession, into which 
all its diameters can be divided, are sunk below the surface, or plane of the 
ecliptic, thus causing the earth's axis to tilt over towards the portions suc- 
cessively submerged, until it finally sweeps entirely round and comes to 
resume its first position. 

But do you now demand what power seizes the earth's protuberant equa- 



irmtiCRSAL graVil 

* 2 ■ " S'^ - ^ 

tor, and tilts it successively towards every point of the compass'?"! answer 

that the power is lodged in the sun and moon, and it is their combined 

action which works out these wonderful results. In case the sun and moon 

were so situated as always to be in the plane of the earth's equator, then 

they would have no power to change the position of the equator. But we 

know that th y are not in this plane, except when passing through it, and 

are found som ^ times on th north and sometimes on the south side of it. 

Wherever either of them may be, the nearest half oi thr requndant matter 

about the earth's equator will be more forcibly attracted than the remote 

half, and the equator will be tilted towards the attracting body, and the 

axis of the earth will follow the movement of the equator to which it is 

firmly fixed. 

Thus does the earth's whole solid mass sway to the motion of the ring 
of matter heaped up around the equator, delicately and beautifully sensitive 
to all the changes in th relative places of the sun and moon. Neither 
the earth nor its axis are ever, for one moment, released from the action of 
these remote bodies. Howev r slight the effects, however varied in action, 
oscillating to every point within certain prescribed limits, the stability is 
preserved, and the final effect is a small retrograde motion of the equinox 
at the end of every year and a slight change in the place of the pole of the 
heavens. 

But there is no isolated matter in the universe. — Every particle of 
matter attracts every other particle of matter, and it is impossible fur the 
sun and moon to ex:rt any influencj on the equatorial ring f matter which 
belongs to our globe, without feeling, in their turn the readijn of this 
ring on themselves. — -The remote and ponderous sun may, in consequence ^f 
of its vast size and distance, escape from any effect capable of being de- 
tected by observation. But this is not the case with the moon. Her 
proximity to the earth and diminutive mass, render her peculiarly sen- 
sitive to the influ nee of the redundant matter at the earth's equator, and as 
her attraction tilts the plane of the earth's equator, so does the equatorial 
ring tilt the plane of the moon's orbit. These effects have been accurately 
observed and measured, and strange to relate, their exact values have ex- 
hibited the figure which belongs to the earth with far greater precision than 
can be obtained from measures on its surface. We may even go farther, 
for such is the intimate relationship between the e&rUi and its attendant 
satellite, that there is scarcely a questi ,n can be asked with reference to 
the one, that is not answered by the other. 

If we demand the weight of the earth when compared with the sun, th<? 
moon answers. If the excess of the equatorial diameter of the earth over 
the polar be required, the moon answers. If the homogenity of the in- 
terior of the solid earth be required, the moon replies, If the thickness of 
the earth's crust is sought for, question the moon, and the answer comes. 
If you would know the sun's distance from the earth, ask the moon. If 



92 stuuctxiue of the univebse. 

the permanency of the axis of rotation be required, ask the moon, and she 
alone yields a satisfactory reply. Finally, if curiosity leads us to inquire 
whether the length of the day and night, the revolution oi the earth on 
its axis, be uniform, or whether it may not have changed by a single second 
in a thousand years, we go to the moon for an answer, and in eacli and 
every instance her replies to all the profound and mysterious questions are 
clear and satisfactory. How wonderful the structure of the universe ! 
How gigantic the power of the human intellect ! If all the stars of heaven 
were struck from existence ; if every planet and satellite which the eye 
and the telescope descry, inside and beyond the earth's orbit, were swept 
away forever, and the sun, earth and moon alone remained for the study 
of man, and as evidences of the being and wisdom of God, in the exquisite 
adjustme ts of this system, in the reciprocal influences of its three bodies, 
in their vast cycles of enfiguration, in their relatives masses, magnitudes, 
distances, motions, and perturbations, there would remain themes suffi- 
ci nt for the exercise of the most exalted genius, and proof of the being 
of God, so dear a- d Dositive, that uo sane mind could comprehend it and 
disbelieve. 



LECTURE VI. 

THE STABILITY OF THE PLANETAEY SYSTEM. 

When, by the application of a single great law, the mind had succeeded 
in resolving the difficult problems presented by the motions of the earth 
and its satellite, the moon, it rose to the examination of the higher and 
more complicated questions of the stability of the entire system of planets, 
satellites, and comets, which are found to pursue their courses round the 
sun. The number of bodies involved in this investigation, their magni- 
tudes and vast periods of revolution, their great distances from the ob- 
server, and the exceeding delicacy of the required observations, combined 
with the high interest which attaches itself to the final result, have united 
to render this investigation the most wonderful which has ever employed 
the energies of the human mind. 

To comprehend the dignity and importance of this great subject, let us 
rapidly survey the system, and moving outward to its known boundaries, 
mark the number and variety of worlds involved in the investigation. 
Beginning, then, at the great centre, the grand controlling orb, the sun, we 
find its magnitude such as greatly to exceed the combined masses of all its 
attendant planets. Indeed, if these could all be arranged in a straight line 
on the same side of the sun, so that their joint effect might be exerted on 
that body, the centre of gravity of the entire system thus located, would 
scarcely fall beyond the limits of the sun's surface. At a mean distance 
of 36,000,000 of miles from the sun we meet the nearest planet, Mercury, 
revolving in an orbit of considerable eccentricity, and completing its cir- 
cuit around the sun in a period of about eighty-eight of our days. This 
world has a diameter of only 3,140 miles, and is the smallest of the old 
planets. Pursuing our journey, at a distance of 68,000,000 of miles from 
the sun, we cross the orbit of the planet Venus. Her magnitude is nearly 
equal to that of the earth. Her diameter is 7,700 miles, and the length 
of her year is nearly 225 of our days. The next planet we meet is the 
earth, whose mean distance from the sun is 95,000,000 of miles. The 
peculiarities which mark its movements and those of its satellite, have 
been already discussed. Leaving the earth, and continuing our journey 
outward, we cross the orbit of Mars, at a mean distance from the sun of 
142,000,000 of miles. This planet is 4,100 miles in diameter, and performs 
its revolution around the sun in about 687 days, in an orbit but little 
inclined to the plane of the ecliptic. Its features, as we shall see here- 



94 STBUCTUBE OF THE UNIVEBSE. 

after, are more nearly like those of the earth than any other planet. Be- 
yond the orbit of Mars, and at a mean distance from the sun of about 
250,000,000 of miles, we encounter a group of small planets, eight in 
number, presenting an anomaly in the system, and entirely different from 
anything elsewhere to be found. These little planets are called asteroids. 
Their orbits are, in general, more eccentric, and more inclined to the 
ecliptic, than those of the other planets ; but the most remarkable fact is 
this: — that their orbits are so nearly equal in size, that when projected on 
a common plane, they are not enclosed, the one within the other, but act- 
ually cross each other. 

We shall return to an examination of these wonderful objects hereafter. 
At a mean distance of 485,000,000 of miles from the sun, we cross the 
orbit of Jupiter, the largest and most magnificent of all the planets. His 
diameter is nearly 90,000 miles. He is attended by four moons, and per- 
forms his revolution round the sun in a period of nearly twelve years. — 
Leaving this vast world, and continuing our journey to a distance of 
890,000,000 of miles from the sun, we cross the orbit of Saturn, the most 
wonderful of all the planets. His diameter is 76,068 miles, and he sweeps 
round the sun in a period of nearly twenty-nine and a half years. He is 
surrounded by several broad concentric rings, and is accompanied by no 
fewer than seven satellites or moons. The interplanetary spaces we per- 
ceive are rapidly increasing. The orbit of Uranus is crossed at a mean 
distance from the sun of 1,800,000,000 of miles. His diameter is 35,000 
miles, and his period of revolution amounts to rather more than eighty-four 
of our years. He is attended by six moons, and pursues his journeys at a 
slower rate than any of the interior planets. Leaving this planet, we 
reach the known boundary of the planetary system, at a distance of 
about 3,000,000,000 of miles from the sun. Here revolves the last dis- 
covered planet, Neptune, attended by one, probably by two moons, and 
completing his vast circuit about the sun in a period of one hundred and 
sixty-four of our years. — His diameter is eight times greater than the 
earth's, and he contains an amount of matter sufficient to form one hun- 
dred and twenty-five worlds such as ours. 

Here we reach the known limit of the planetary worlds, and standing at 
this remote point and looking back towards the sun, the keenest vision of 
man could not descry more than one solitary planet along the line we 
have traversed. The distance is so great, that even Saturn and Jupiter 
are utterly invisible, and the sun himself has shrunk to be scarcely greater 
than a fixed star. 

There are certain great characteristics which distinguish this entire 
scheme of worlds. They are all nearly globular — they all revolve on 
axes — their orbits are all nearly circular — they all revolve in the same 
direction around the sun — the planes of their orbits are but slightly in- 
clined to eack other, and their moons follow the same general laws. With 



STABILITY OF THE PLANETARY SYSTEM. f 5 

a knowledge of these general facts, it is proposed to trace the reciprocal 
influences of all these revolving worlds, and to learn, if it be possible 
whether this vast scheme has been so constructed as to endure while time 
shall last, or whether the elements of its final dissolution are not contained 
within itself, either causing the planets, one by one, to drop into the sun, 
or to recede from this great centre, released from its influence, to pursue 
their lawless orbits through unknown regions of space. 

Before proceeding to the investigation of the great problem of the sta- 
bility of the universe, let us examine how far the law of gravitation ex- 
tends its influence over the bodies which are united in the solar system. 
A broad and distinct line must be drawn between those phenomena, for 
which gravitation must render a satisfactory account, and those other 
phenomena, for which it is in no wise responsible. In the solar system 
we find, for example, that all the planets revolve in the same direction 
around the sun, in orbits slightly elliptical, and in planes but little in- 
clined to each other. Neither of these three peculiarities is in any way 
traceable to the law of gravitation. 

Start a planet in its career, and, no matter what be the eccentricity of 
its orbit, the direction of its movement, or the inclination of the plane in 
which it pursues its journey, once projected, it falls under the empire of 
gravitation, and ever after, this law is accountable for all its movements. 
We are not, therefore, to regard the remarkable constitution of the solar 
system as a result of any of the known laws of nature. 

If the sun were created, and the planetary worlds formed and placed at 
the disposal of a being possessed of less than infinite wisdom, and be were 
required so to locate them in space, and to project -them in orbits, such 
that their revolutions should be eternal, even with the assistance of the 
known laws of motion and gravitation, this finite being would fail to 
construct his required system. 

Let it be remembered, that each and every one of these bodies exerts 
an influence upon all the others. There is no isolated object in the 
system. Planet sways planet, and satellite bends the orbit of satellite, 
until the primitive curves described, lose the simplicity of their character, 
and perturbations arise, which may end in absolute destruction. There is 
no chance work in the construction of our mighty system. Every planet 
has been weighed and poised, and placed precisely where it should be. 
If it were possible to drag Jupiter from its orbit, and cause him to change 
places with the planet Venus, this interchange of orbits would be fatal to 
the stability of the entire system. In contemplating the delicacy and 
complexity of the adjustment of the planetary worlds, the mind cannot 
fail to recognize the fact that, in all this intricate balancing, there is a 
higher object to be gained than the mere perpetuity of the system. 

If stability had been the sole object, it might have been gained by a far 
gimpler arrangement. If God had so constituted matter that the sun 



96 STRUCTURE OF THE UNIVERSE. 

might have attracted the planets, while these should exert no influence 
over each other — that the planets might have attracted their satellites, 
while these were free from their reciprocal influences — then, indeed, a 
system would have been formed, whose movements would have been 
eternal, and whose stability would have been independent of the relative 
positions of the worlds, and the character of their orbits. Give to them but 
space enough in which to perform their revolutions around the sun, so 
that no collisions might occur, freed from this only danger, every planet, 
and every satellite, will pursue the same undeviating track throughout 
the ceaseless ages of eternity. 

If this statement be true, it may be demanded, why such a system was 
not adopted. It is impossible for us to assign all the reasons which led to 
the adoption of the present complicated system. Of one thing, however, 
we are certain : — If God designed that in the heavens his glory and his 
wisdom should be declared, and that in the study of his mighty works, 
his intelligent creatures should rise higher and higher towards his eternal 
throne, then, indeed, has the present system been admirably constituted 
for the accomplishment of this grand design. To have acquired a knowl- 
edge of a system constituted of independent planets, free from all mutual 
perturbations, would have required scarcely no effort to the mind, when 
compared with that put forth in the investigation of the present complex 
construction of the planetary system. The mind would have lost the 
opportunity of achieving its greatest triumphs, while the evidence of 
infinite wisdom displayed in the arrangement and counterpoising of the 
present system would have been lost forever. There is one other thought 
which here suggests itself with so much force that I cannot turn away 
from it. We speak of gravitation as some inherent quality or property of 
matter, as though matter could not exist in case it were deprived of this 
quality. This is, however, a false idea. Matter might have existed 
independent of any quality which should cause distant globes to influence 
each other. — This force called gravitation, even admitting that it must 
have an existence, no special law of its action could have forced itself on 
matter to the exclusion of all other laws. Why does this force diminish 
as the square of the distance at which it operates, increases f There are 
almost an infinite number of laws, according to which an attraction might 
have exerted itself, but there is no one which would have rendered the 
planets fit abodes for sentient beings, such as now dwell on them, and 
which would at the same time have guaranteed the perpetuity of the 
system. Admitting, then, that matter cannot be matter, without exert- 
ing some influence on all other matter, (which I am unwilling to admit), 
in the selection of the law of the inverse square of the distance, there is 
the strongest evidence of design. 

If we rise above the law of gravitation to the Great Author of nature, 
and regard the laws of motion and of gravitation as nothing more than 



STABILITY OF THE PLANETARY SYSTEM. 97 

the uniform expressions of his will, we perceive at once the impossibility 
of constructing the universe in such manner that the^sun should attract 
the planets, without these attracting each other ; or that the planets 
should attract their satellites without, in turn, being reciprocally influ- 
enced by their satellites ; for this would be equivalent to saying that the 
will of the same Almighty Being should exert itself, and not exert itself, 
at the same moment, which is impossible. As there is but one God, so 
there is but one kind of matter, governed by one law, applied by infinite 
wisdom to the formation of suns and systems without number, crowding 
the illimitable regions of space, all moving harmoniously, fulfilling their 
high destiny, and all sustained by the single arm of divine Omnipotence. 

We now proceed to an examination of the great question, Is the system 
of worlds by which we are surrounded, and of which our earth and its 
moon form a part, so constructed that, under the operation of the known 
laws of nature, it shall forever endure, without ever passing certain 
narrow limits of change, which do not any way involve its stability ? 

It is well known that the planets revolve in elliptical orbits of small 
eccentricity — that under the action of the primitive impulse by which 
they were projected in their orbits, they would have moved off in a straight 
line, with a velocity proportioned to the intensity of the impulse, and 
which would have endured forever ; but being seized by the central 
attraction of the sun, at the moment of starting in their career, the joint 
action of these two forces, bends the planet from its straight direction, 
and cause it to commence a curvilinear path, which carries it round the 
sun. 

The question which first presents itself is this : — If the central force 
lodged in the sun has the power to cause a planet to diverge from the 
straight line in which, but for this, it would have moved — if it draw it 
into a curved path, will not this central force, which is ever active, finally 
overcome, entirely, the impulsive force originally given to the planet, 
draw it closer and closer to the sun in each successive revolution, in a 
spiral orbit, until, finally, the planet shall fall into the sun, and be destroyed 
forever? This question arises independent of the extraneous influence 
which the planets exert over each other. It refers to a solitary globe re- 
volving around the sun, under the influence of a central force which varies 
its action as does the kw of gravitation. The problem has been submitted 
to the most rigorous mathematical examination, and a result has been 
obtained which settles the question in the most absolute manner. The 
amount by which the central force, in a moment of time, overcomes the 
effect produced by the primitive impulse, is a quantity, infinitely small 
and of the secona order. If it were found to be infinitely small in each 
moment of time, then might it accumulate so that, at the end of a vast 
period, it might become finite and appreciable. But because it is of the 
second order of infinitely small quantities, before it can become an infinitely 



98 STRUCTURE OF THE UNIVERSE. 

small quantity of the first order, a period equal to infinite ages must roll 
by, and to make a finite appreciable quantity out of this, an infinite cycle 
of years must roll round an infinite number of times ! 

Such is the answer given by analysis to this wonderful question. " Is 
there no change ? " demands the astronomer. " Yes," answers the all- 
seeing analysis. " When will it become appreciable ? " asks the astron- 
omer. " At the end of a period infinitely long, repeated an infinite number 
of times," is the reply. 

Having settled this important question, it remains now to examine 
whether the mutual attractions of the planets on each other may not, in 
the end, change permanently the form of their orbits, and lead, ultimately, 
to the destruction of the system. To comprehend more readily the 
nature of the examination, let us review the points involved in the per- 
manency of our orbit. 

Take, for example, our own planet, the earth. It now revolves in an 
elliptic orbit, whose magnitude is determined by the length of its longer 
axis, and by its eccentricity. These elements are readily deduced from 
observation. If it were possible to construct this orbit of some material, 
like wire, which would permit us to take it up and locate it in space at 
will, to enable us to give it the position now occupied by the actual orbit 
of the earth, we must first carry its focus to the sun's centre ; we must 
then turn its longer axis around this centre as a fixed point, until the 
nearest vertex of the wire orbit shall fall upon that point of the earth's 
orbit which is at this time nearest to the sun. Having accomplished this, 
the axes will coincide in their entire length, and to make the orbits coin- 
cident, we must revolve the artificial one around the now common axis, 
until its plane shall fall upon the actual orbit of the earth. 

If, now, change should ever come, in the absolute coincidence of these 
two orbits, regarding the iron one as fixed and permanent, the orbit of 
nature may vary from it in any one or all of the following ways : — 
First. The natural orbit, all other things remaining the same, may 
leave the fixed orbit by a variation of eccentricity ; — that is, it may 
become more or less nearly circular. Second. The planes of the orbits 
remaining coincident, the curves may separate from each other, in con- 
sequence of an angular movement of the longer axis of the natural orbit, 
by means of which the vertex of the natural curve shall be carried to the 
right or to the left of the vertex of the fixed one. Third. While these 
causes are operating to produce change, an increase of deviation may be 
occasioned by the fact that the two planes may become inclined to each 
other, thus causing the natural orbit to lie partly above and partly below 
the fixed one. — These, then, are the several ways in which the orbits of 
the planets may change ; and to settle the question of stability, we must 
ascertain whether these changes actually exist, and whether any of them, 
in case they do exist, and are progressing constantly in the same direction, 



STABILITY OF THE PLANETARY SYSTEM. 99 

will ever prove fatal to the permanency of the system, finally accomplishing 
its absolute destruction, or rendering it unfit for the sustentation of that 
life which now exists upon the planet. 

By a close examination of this great subject, both theoretically and 
practically, it is found that the system is so constituted, that not a single 
planet or satellite revolves in an orbit absolutely invariable. Theory 
demonstrates that such changes must exist, and observation confirms this 
great truth, by showing that they actually do exist. 

Draw, in imagination, a straight line from the sun's centre, through 
the perihelion, or nearest point to the sun of the earth's orbit, and let it 
be extended to the outermost limits of the entire system. On this locate 
the perihelion points of the orbits of all the planets, in these points fix the 
planets themselves. They are now all on the same side of the sun, the 
longer axes of their orbits are in the same direction, and they are all 
located at their nearest distance, from the sun, or in perihelion. The 
planes of the orbits are inclined to each other under their proper angles, 
and they all intersect in a common line of nodes passing through the 
sun's centre. Now give the entire group of planets their primitive im- 
pulse, and at the same instant they start in their respective orbits round the 
sun. Now, in case no perturbations existed, the perihelion points, the in- 
clinations, and the lines of nodes, would remain fixed forever, and al- 
though millions of years might pass away before the planets would again 
resume their primitive position with reference to each other, yet the time 
would come when a final restoration would be effected. 

At the end of 164 years, Neptune will have completed its revolution 
round the sun, and will return to its starting point. All the other planets 
will have performed several revolutions, but each, on reaching the point 
of departure, will find the perihelion of its orbit changed in position, the 
inclination altered and the line of nodes shifted. These changes continue 
until the longer axes of the orbits, which once coincided, radiate from the 
sun in all directions. The lines of nodes, once common, now diverge 
under all angles, the inclinations increasing or decreasing, and even the 
figures of the orbits undergoing constant mutation ; and the grand ques- 
tion arises, whether these changes, no matter how slow, are ever to con- 
tinue progressing in the same direction, until all the original features of 
the system shall be effaced, and the possibility of return to the primitive 
condition destroyed forever. 

Such a problem would seem* to be far too deep and complicated ever to 
be grasped by the human intellect. It is true that no single mind was able 
to accomplish its complete solution, but the advance made by one has 
been steadily increased by another, until, finally, not a question remains 
unanswered. The solution is complete, yielding results of the most won- 
derful character. 

We shall examine this great problem in detail, and commence with the 
figure of the orbit of any planet, our earth, for example. 



100 STMUCTUBE OF THE UNIVEBSE. 

The amount of heat received from the sun by the earth depends, other 
things being the same, on the minor axis of its ecliptic orbit. Any change 
in the eccentricity operates directly to increase or decrease the shorter 
axis, and consequently to increase or decrease the mean annual amount of 
heat received from the sun. Now we know that animal and vegetable 
life is adjusted in such way that it requires almost exact uniformity in the 
mean annual amount of heat which it shall enjoy. An increase or decrease 
of two or three degrees in. temperature would make an entire revolution 
in the animals and plants belonging to the region experiencing such a 
change. If, then, it be true that the eccentricity of the earth's orbit is 
actually changing, under the combined action of the other planets, may this 
change continue so far as to subvert the order of nature on its surface ? — 
This question has been answered in the most satisfactory manner. 

It is found that the greater axes of the planetary orbits are subjected to 
slight and temporary variations, returning, in comparatively short periods, 
to their primitive values. This important fact guarantees the permanency of 
the periodic times, so that it becomes possible to deduce, with the utmost pre- 
cision, the periodic times of the planets, from the mean of a large number of 
revolutions. That of the earth is now so accurately known, and so absolutely 
invariable, that we know what it will be a million of years hence, should 
the system remain as it now is, as perfectly as at the present moment. But 
neither of these elements secures the stability of the eccentricity, or of the 
minor axis. Lagrange, however, demonstrated a relation between the 
masses of the planets, their major axes and eccentricities, such, that while 
the masses remain constant, and the axes invariable, their eccentricity can 
only vary its value through extremely narrow limits. These limits have 
been assigned, beyond which the change can never pass, and within these 
narrow bounds we find the orbits of all the planets sloAvly vibrating back- 
ward and forward, in periods which actually stun the imagination. 

This remarkable law for the preservation of the system would not hold 
in any other organization. It demands orbits nearly circular, with planes 
nearly coincident, with periodic times related as are those of the planets, 
and the planets themselves located as they actually are. No interchange 
of orbits is admissible ; but, constituted as the system now is, the perpetuity 
is absolutely certain, so far as the change of eccentricity is concerned. 

Let us now examine the changes which affect the position of the major 
axis in its own plane. The perihelion of every orbit is found to be slowly 
advancing. Nor is this advance ever to be changed into a retrograde 
motion. The movement is ever progressive in the same direction, and the 
perihelion points of all the orbits are slowly sweeping round the sun. — 
That of the earth's orbit accomplishes its revolution in one hundred and 
eleven thousand years ! How wonderful the fact, that such discoveries 
should be made by man, whose entire life is but a minute fraction of these 
vast periods of time ! 



STABILITY OF THE PLANETARY SYSTEM. 101 

Owing to a retrograde motion in the vernal equinox, carrying it around 
in the opposite direction in 25,868 3-ears, the perihelion and equinox pass 
each other once in 20,984 years. Knowing their relative positions at this 
moment, and their rates of motion it is easy to compute the time of their 
coincidence. Their last coincidence took place 4,089 years before the 
Christian era, or about the epoch usually assigned for the creation of man. 
The effect of the coincidence of the perihelion with the vernal equinox, is 
to cause an exact equality in the length of spring and summer, compared 
with autumn and winter. In other language, the sun will occupy exactly 
half a year in passing from the vernal to the autumnal equinox, and the 
other half in moving from the autumnal to the vernal equinox. 

At present, the line of equinoxes divides the earth's elliptic orbit into 
two unequal portions. The smaller part is passed over in the fall and 
winter, causing the earth to be nearer the sun at this season than in sum- 
mer, and making a difference in the length of the two principal seasons, 
summer and winter, of some seventeen and a half days. This inequality, 
which is now in favor of summer, will eventually be destroyed, and the 
time will come when the earth will be farthest from the sun during the 
winter, and nearest in the summer. But at the end of a great cycle of 
more than 20,000 years, all the changes will have been gone through, and, 
in this respect, a complete compensation and restoration will have been 
effected. 

This epoch of subordinate restoration will find the perihelion of the 
earth's orbit located in space far distant from the point primitively occu- 
pied. Five of these grand revolutions of 20,984 years mast roll round 
before the slow movement of the perihelion shall bring it back to its start- 
ing point. 110,000 years will then restore the axis of the earth's orbit, 
and the equinoctial line, nearly to their relative positions to each other, 
and to the same region of absolute space occupied at the beginning of this 
grand cycle. 

If, now, we direct our attention to the other planets, we find their peri- 
helion points all slowly advancing in the same direction. That of the orbit 
of Jupiter performs its revolution round the sun in 186,207 years, while 
the perihelion of Mercury's orbit occupies more than 200,000 years in 
completing its circuit round the sun. To effect a complete restoration of 
the planetary orbits to their original position, with reference to their peri- 
helion points, will require a grand compound cycle, amounting to" millions 
of years. Yet the time will come when all the orbits will come again to 
their primitive positions, to start once more on their ceaseless journeys. 

In the changes of the eccentricities, it will be remembered, the stability 
of the system was involved. Should these changes be ever progressive, no 
matter how slowly, a time would finally come when the original figure of 
the orbit would be destroyed, the planet either falling into the sun, or 
sweeping away into unknown regions of space. But a limit is assigned, 



102 STRUCTURE OF THE UNIVERSE. 

beyond which the change can never pass. — Some of the planetary orbits 
are becoming more circular, others growing more elliptical ; but all have 
their limits fixed. The earth's orbit, for example, should the present rate 
of decrease of eccentricity continue, in about half a million of years will 
become an exact circle. There the progressive motion of the changes 
stops, and it slowly commences to recover its ellipticity. This is not the 
case with the motions of the perihelia. Their positions are in no way involved 
in the well being of a planet, or in its capacity to sustain the life which 
exists on its surface ; and since the stability of the system is not endan- 
gered by progressive change, it ever continues in the same direction, until 
the final restoration is effected, by an entire revolution about the sun. 

Let us now examine the inclinations of the planetary orbits. Here it is 
found that there is no guarantee for the stability of the system, provided 
the angles under which the orbits of the planets are inclined to each other 
do not remain nearly the same forever. — If changes are found to exist, by 
which the inclinations are made to increase, without stopping and return- 
ing to their primitive condition, then is the perpetuity of the system ren- 
dered impossible. Its fair proportions must slowly wear away, the harmony 
which now prevails be destroyed, and chaos must come again. 

Commencing again with the earth, we find that, from the earliest ages, 
the inclination of the earth's equator to the ecliptic has been decreasing. 
Since the measure of Eratosthenes, 2,078 years ago, the decrease 1ms 
amounted to about 23' 44 ', or about half a second every year. Should 
the decrease continue, in about 85,000 years the equator and ecliptic would 
coincide, and the order of nature would be entire lv changed ; — perpetual 
spring would reign throughout the year, and the seasons would be lost 
forever. Of this, however, there is no danger. The diminution will reach 
its limit in a comparatively short time, when the decrease of inclination 
will change into an increase, and thus slowly rocking backwards and for- 
wards in thousand of years, the seasons shall ever preserve their appointed 
places, and seed time and harvest shall never fail. These changes of in- 
clination are principally due to the perturbations of Venus, and arising 
from configurations, will be ultimately entirely compensated. 

The angles under which the planetary orbits are inclined to each other 
are in a constant state of mutation. The orbit of Jupiter at this time forms 
an angle with the ecliptic of 4,731 seconds, and this angle is decreasing at 
such a rate that, in about 20,000 years the planes would actually coincide. 
This would not effect the well being of the planets or the stability of the 
system, but should the same change now continue, the angle between the 
orbits might finally come to fix them even at right angles to each other, 
and a subversion of the present system would result. 

A profound investigation of the problem of the planetary inclinations, 
accomplished by Lagrange, resulted in the demonstration of a relation 
between the masses of the planets, the principal axes of their orbits, and 



STABILITY OF THE PLANETARY SYSTEM. 103 

the inclinations, such that, although the angles of inclination may vary, 
the limits are narrow, and they are all found slowly to oscillate about their 
mean positions, never passing the prescribed limits, and securing, in this 
particular, the perpetuity of the system. 

Here, again, we are presented with the remarkable fact, that whenevei 
mutation involves stability, this mutation is of a compensatory character, 
always returning upon itself, and, in the long run, correcting its own effects. 
If all this mighty system was organized by chance, how happens it that 
the angular motions of the perihelia of the planetary orbits are ever pro- 
gressive, while the angular motions of the planes of the orbits are vibrat- 
ing ? Design, positive and conspicuous, is written all over the system, in 
characters from which there is no escape. 

We now proceed to an examination of the lines in which the planes of 
the planetary orbits cut each other, or the lines in which they intersect a 
fixed plane. These are called the lines of nodes. They all pass through 
the sun's centre, and, in case they ever were coincident, they now radiate 
from a common point in all directions. 

Here is an element in no degree involving in its value the stability of the 
system, and from analogy we already begin to anticipate that its changes, 
whatever they may be, will probably progress always in the same direc- 
tion. This is actually the case. The nodes of the planetary orbits are all 
slowly retrograding on a fixed plane, and in vast periods, amounting to 
thousands of years, accomplish revolutions, which, in the end, return them 
to their primitive positions. 

Thus are we led to the following results. Of the two elements which 
fix the magnitude of the planetary orbits, the principal axes, and the ec- 
centricity, the axes remain invariable, while the eccentricity oscillates be- 
tween narrow and fixed limits. In the long run, therefore, the magnitudes 
of the orbits are preserved. 

Of the three elements which give position to the planetary orbits, viz : 
the place of the perihelion, the lines of nodes, and the inclinations, the 
two first ever vary in the same direction, and accomplish their restoration 
at the end of vast periods of revolution, while the inclinations vibrate 
between narrow and prescribed limits. 

One more point, and we close this wonderful investigation. The last 
question which presents itself is this : — May not the periodic times of the 
planets be so adjusted to each, as that the results of certain configurations 
may be ever repeated without any compensation, and thus, by perpetual 
accumulation, finally effect a destruction of the system? 

If the periodic times of two neighboring planets were exact multiples of 
the same quantity, or if the one was double the other, or in any exact ratio, 
then the contingency would arise, above alluded to, and there would be 
perturbations which would remain uncompensated. A near approach to 
this condition of things actually exists in the system, and gave great 



104 STRUCTURE OF THE UNIVERSE. 

trouble to geometers. It was found, on comparing observations, that the 
mean periods of Jupiter and Saturn were not constant — that one was on 
the decrease, while the other was on the increase. This discovery seemed 
to disprove the great demonstration which had fixed as invariable the 
major axes of the planetary orbits, and guaranteed the stability of the 
mean motions. It was not until after Laplace had instituted a long and 
laborious research, that the phenomenon was traced to its true origin, and 
was found to arise from the near commensurability of the periodic times 
of Jupiter and Saturn — five of Jupiter's periods being nearly equal to two 
of Saturn's. In case the equality were exact, it is plain that if the two 
planets set out from the same straight line drawn from the sun, at the end 
of a cycle of five of Jupiter's periods, or two of Saturn's, they would be 
again found in the same relative positions, and whatever effect the one 
planet had exerted over the other would again be repeated under the same 
precise circumstances. Hence would arise derangements which would 
progress in the same direction, and eventually lead to permanent derange- 
ment of the system. 

But it happens that five of Jupiter's periods are not exactly equal to two 
of Saturn's, and in this want of equality safety is found. The difference 
is such, that the point of conjunction of the planets does not fall at the 
same points of their orbits, but at the end of each cycle is in advance by a 
few degrees. Thus the conjunction slowly works round the orbits of the 
planets, and, in the end, the effect produced on one side of the orbit is 
compensated for on the other, and a mean period of revolution comes out 
for both planets, which is invariable. In the case of Jupiter and Saturn, 
the entire compensation is not effected until after a period of nearly a 
thousand years. 

A similar inequality is found to exist between the earth and Venus 
with a period much shorter, and producing results much less easily ob- 
served. In no instance do we find the periods of any two planets in an 
exact ratio. They are all incommensurable with each other, and in this 
peculiar arrangement we find the stability of the entire system is secured. 

So far, then, as the organization of the great planetary system is con- 
cerned, we do not find within itself the elements of its own destruction. 
Mutation and change are everywhere found — all is in motion — orbits ex- 
panding or contracting — their planes rocking up and down — their peri- 
helia and nodes sweeping in opposite directions round the sun, — but the 
limits of all these changes are fixed ; — these limits can never be passed, and 
at the end of a vast period, amounting to many millions of years, the entire 
range of fluctuation will have been accomplished, the entire system, planets, 
orbits, inclinations, eccentricities, perihelia, and nodes, will have regained 
their original values and places, and the great bell of eternity will have 
then sounded one. 

Having reached the grand conclusion of the stability of the system of 



STABILITY OF THE PLANETARY SYSTEM. 105 

planets, in their reciprocal influences, and that no element of destruction 
is found in the organization, we propose next to inquire whether the same 
features are stamped on the subordinate groups composing the planetary 
system. — As our limits will not permit us to enter into a full examination 
of all the subordinate groups, we shall confine our remarks to our own 
earth and its satellite, Jupiter and his satellites, and to Saturn, his rings 
and moons, We shall, in this examination, find it praticable to answer, 
to some extent, the inquiry as to whether either of these systems has re- 
ceived any shock from external causes. We know nothing as to the future, 
and can, in this particular, only form our conjectures as to what is to be, 
from what has been. 

We commence our inquiry by an examination of two questions, viz : — 
Is the velocity of rotation of the earth on its axis absolutely invariable ? 
Has the relation between the earth and moon ever been disturbed by any 
external cause ? There is nothing so important to the well-being of our 
planet and its inhabitants as absolute invariability in the period of its 
axical rotation. The sidereal day is the great unit of measure for time, 
and is of the highest consequence in all astronomical investigations. If 
causes are operating, either to increase or decrease the velocity of 
rotation, a time will come when the earth will cease to rotate, or else ac- 
quire so great a velocity as to destroy its figure, and in the end, scatter its 
particles in space. 

It is difficult to ascertain from theory a perfectly satisfactory answer 
to the question of the invariable velocity of rotation of the earth, but 
Laplace has demonstrated that the length of the day has not varied by 
the hundredth of one second during the last two thousand years — that 
is, the length of the day is neither greater nor less than it was two thou- 
sand years ago by the hundreth of a second. The reasoning leading 
to this remarkable result is simple, and may be readily comprehended 
by all. Two thousand years ago, the duration of the moon's period of 
revolution around the earth was accurately determined, and was expressed 
in days and parts of a day. The measure of the same period has been ac- 
complished in our own time, and is expressed in days and parts of a day. 
Now all the causes operating to change the moon's period of revolution 
are known, and may be applied. When this is done it is found that the 
moon's period now and two thousand years ago, agree precisely, being ac- 
complished in the same number of da}*s and parts of a day — which would 
be impossible, if the unit of measure, the day, had varied ever so slightly. 

The extraordinary relation existing between the moon's period in her 
orbit and the time occupied in her axical rotation, gives us the opportunity 
of ascertaining whether our system has received any external shock. These 
two periods are so accurately adjusted, that in all respects an exact 
euqality exists. The moon ever turns the same hemisphere to the earth, 
and ever will, unless some external cause should arise to disturb the per- 



106 STRUCTURE OF THE UNIVERSE. 

feet harmony which now reigns. It it not my purpose to explain why it 
is that this phenomenon exists. I merely desire to state, that this delicate 
balancing of periods furnishes an admirable evidence that, for several 
thousands of years, at least, no shock has been received by the earth and 
its satellite. Steadily have they moved in their orbits, subject only to 
the influence of causes originating in the constitution of the mighty system 
of which they constitute a part. 

Moving out to a more complex system, we find in the remarkable ar- 
rangement of the satellites of Jupiter, a delicate test for the action of sudden 
and extraneous causes. Here we find the periodic times of the satellites 
so related, that a thousand periods of the first, added to two thousand 
periods of the third, will be precisely equal to three thousand periods of 
the second. This delicate balancing of periods would be destroyed by 
the action of any external shock, such as might be experienced from the 
collision of a comet sweeping through the system. Thus far, we know 
that no disturbance has entered, and a knowledge of facts will now pass 
down to posterity, which will give the means of ascertaining exactly the 
influence of all disturbing causes which do not form a part of the great 
system. 

The last subordinate group, and the most extraordinary one to which I 
will at this time direct your attention, is that of Saturn and his rings. 
Here we find a delicacy of adjustment and equilibrium far exceeding any 
thing yet exhibited in our examinations. This great planet is surrounded 
certainly by two, probably by three immense rings, which are formed of 
solid matter, in all respects like that constituting the central body. These 
wonderful appendages are nowhere else to be found, throughout the entire 
solar system, at least with certaint}^. Their existence has elsewhere been 
suspected, but around Saturn they are seen with a perfection and dis- 
tinctness which defies all skepticism as to their actual existence. The di- 
ameter of the outer ring is no less than 176,000 miles. Its breadth is 21,000 
miles, while its thickness does not exceed one hundred miles. The inner ring 
is separated from the outer one by a space of aboutl,800 miles, — its breadth 
34,000 miles, its inner edge being about 20,000 miles from the surface of 
the planet. — Its thickness is the same as that of the outer ring. These ex- 
traordinary objects are rotating in the same direction as the planet, and 
with a velocity so great that objects on the exterior edge of the outer 
ring are carried through space with the amazing velocity of nearly 50,000 
miles an hour, or nearly fifty times more swiftly than the objects on the 
earth's equator. 

What power of adjustment can secure the stability of these stupendous 
rings? No solid bond fastens them to the planet — isolated in space, they 
hold their places, and revolving with incredible velocity around an imag- 
inary axis, they accompany their planet in its mighty orbit round the sun. 
Such is the exceeding delicacy with which this system is adjusted, that, 



STABILITY OF THE PLAKETAUY SYSTEM. 107 

the slightest external cause once deranging the equilibrium, no readjust- 
ment would be effected. The rings would be thrown on the body of the 
planet, and the system would be destroyed. 

To understand the extraordinary character of this system, we will ex- 
plain a little more fully the three different kinds of equilibrium. The 
first is called an equilibrium of instability, and is exemplified in the effort 
to balance a rod on the tip of the finger. The slightest deviation from 
the exact vertical, increases itself constantly, until the equilibrium is 
destroyed. — In case the same rod be balanced on its centre on the finger, 
it presents an example of an equilibrium of indifference ; that is, if it be 
swayed slightly to the one side or the other, there is no tendency to restore 
itself, or to increase its deviation. — It remains indifferent to any change. 
Take the same rod, and suspend it like a pendulum. Now cause it to, 
deviate from the vertical to the right or left, and it returns of itself to the 
condition of equilibrium. This is an equilibrium of stability. We have 
already seen that this is the kind of equilibrium which exists in the 
planetary system. There are constant deviations, but a perpetual effort 
is making to restore the object to its primitive condition. 

Now in case the rings of Saturn are homogeneous, equally thick, and 
exactly concentric with the planet, their equilibrium is one of instabilit}^. 
The smallest derangement would find no restorative power, and would 
even perpetuate and increase itself, until the system is destroyed. For a 
long time it was believed that the rings were equally thick, and concentric 
with the planet, but when it was discovered that such features would 
produce an equilibrium of instability, and that there existed no guarantee 
for the permanency of this exquisite system, an analytic examination was 
made, which led to this singular result, viz : — To change the equilibrium 
of instability into one of stability, all that is necessary is to make the ring 
thicker or denser in some parts than in others, and to cause its centre of 
position to be without the centre of the planet, and to perform around 
that centre a revolution in a minute orbit. Finding these conditions 
analytically, it now became a matter of deep interest to ascertain whether 
these conditions actually existed in nature. The occasional disappearance 
of the ring, in consequence of its edge being presented to the eye of the 
observer, gave a capital opportunity of determining whether it was of uni< 
form thickness. On these rare occasions, in the most powerful telescopes, 
the ring remains visible edgewise, and looks like a slender fibre of silver 
light drawn across the diameter of the planet. In the gradual wasting 
away of the two extremities of the ring, it has been remarked, that the 
one remains visible longer than the other. As the ring is swiftly revolving 
neither extremity can, in any sense, be regarded as fixed, and hence some- 
times the one, some times the other, fades first from the sight. An ex- 
actly uniform thickness in the ring would render such a phenomenon im- 
possible, and hence we conclude, that the first condition of stability is ful- 
filled,-^the rings are net equally thick throughout. 



108 &TRTTCTUB& OP T&M UNIVERSE. 

The micrometer was now applied to detect an eccentricity in the central 
point of the ring. Kecent examinations by Struve and Bessel have settled 
this question in the most satisfactory manner. The centre of the ring 
does not coincide with that of the planet, and itis actually performing a 
revolution around the centre of the planet in a minute orbit, thus forming 
the second delicate condition of equilibrium. The analogy of the great 
system is unbroken in the subordinate one. For more than two hundred 
years have these wonderful circles of light whirled in their rapid career 
under the eye of man, and freed from all external action, they are so 
poised that millions of years shall in nowise effect their beautiful organi- 
zation. Their graceful figures and beautiful light shall greet the eyes of 
the student of the heavens when ten thousand years shall have rolled 
away. 

Thus do we find that God has built the heavens in wisdom, to declare 
his glory, and to show forth his handiwork. There are no iron tracks, 
with bars and bolts, to hold the planets in their orbits. Freely in space 
they move, ever changing, but never changed ; poised and balancing ; 
swaying and swayed ; disturbing and disturbed, onward they fly, fulfilling 
with unerring certainty their mighty cycles. The entire system forms one 
grand complicated piece of celestial machinery ; — circle within circle ; wheel 
within wheel ; cycle within cycle : — revolution so swift as to be completed 
in a few hours ; movements so slow that their mighty periods are only 
counted by millions of years. Are we to believe that the Divine Architect 
constructed this admirably adjusted system to wear out, and to fall in ruins 
even before one single revolution of its complex scheme of wheels had been 
performed ? No. — I see the mighty orbits of the planets slowly rocking to 
and fro, their figures expanding and contracting, their axes revolving in 
their vast periods ; but stability is there. Every change shall wear away, 
and after sweeping through the' grand cycle of cycles, the / 

6hall return to its primitive condition of perfection and beauty. 



LECTURE VIL 

THE DISCOVERY OF NEW PLANETS. 

In the earliest ages of the world, the keen vision of the old astronomers 
had detected the principal members of the planetary system. Even Mer- 
cury, which habitually hovers near the sun, and whose light is almost con- 
stantly lost in the superior brilliancy of that luminary, did not escape the 
eagle glance of the primitive students of the stars. For many thousand 
years no suspicion arose in the mind, as to the existence of other planets, 
belonging to the great scheme, and which had remained invisible from their 
immense distance or their, minute dimensions.— -Indeed the grand investiga- 
tions which have recently engaged our attention, the mutation of the 
planetary orbits, their perpetual oscillations and final restoration, the 
equilibrium of the whole system, had been prosecuted and completed before 
the mind gave itself seriously to the contemplation of invisible worlds. 

The singularly inquisitive genius of Kepler, over whom analogy seems 
to have ever played the tyrant, in an examination of the interplanetary 
spaces, finding these to increase with regularity in proceeding outward 
from the sun, until reaching the space between Mars and Jupiter, which 
was out of all proportion too great, conceived the idea that an invisible 
planet revolved in this space, and thus completed the harmony of the 
system. The space from the orbit of Mercury to that of Venus is 31,000,- 
000 of miles ; from the orbit of Venus to that of the earth is 27,000,000 of 
miles ; from the earth's orbit to that of Mars is 50,000,000 of miles, but 
between the orbit of Mars and that of Jupiter, there exists the enormous 
interval of 359,000,000 of miles. The order is again resumed between the 
orbits of Jupiter and Saturn, and from these slender data Kepler boldly 
predicted that a time would come when a planet would be found interme- 
diate between the orbits of Mars and Jupiter, whose discovery would 
establish a regular progression in the interplanetary spaces. For nearly 
two hundred years this daring speculation was regarded as one of the wild 
dreams of a great, but visionary mind. 

Towards the close of the eighteenth century, when the planetary orbs 
had been studied with great care, and a comparatively accurate knowl- 
edge of their perturbations had been reached, certain unexplained irregu- 
larities gave rise to the suspicion that the movements of Saturn might be 
disturbed by the action of an unknown planet revolving in a vast orbit, 
remote from, and far beyond that of Saturn. These speculations led to no 



110 STRUCTURE OF THE UNIVERSE. 

serious results, and it was only by a fortunate accident that, on the 13th 
of March, 1781, Sir William Herschel noticed a small star of remarkable 
appearance, which happened to fall in the field of his telescope. On apply- 
ing a greater magnifying power, the strange star showed unequivocal 
symptoms of increased dimensions. Its position among the neighboring 
stars was noticed with care, and by an examination on the following even- 
ing, the stranger was found to have sensibly changed position. A few 
nights sufficed to establish the fact that the newly discovered body was 
actually a wandering star, and not for a moment dreaming of the discovery 
of a new planet, Herschel announced to the world that he had found a re- 
markable comet. Efforts were made to obtain the orbit of the stranger, on 
the hypothesis, that like those of all the then known comets, it was extremely 
elongated. Maskelyn and Lexell soon reached the conclusion that no ec- 
centric orbit could possibly represent the motions of the newly discovered 
star, and on a close and diligent examination, it was at last discovered to 
be a primary planet, revolving in an orbit nearly circular, and almost coin- 
cident with the plane of the ecliptic. Its motion was progressive, like the 
other planets, and its vast orbit was only completed at the end of eighty- 
four of our years. Its distance from the sun was found to be no less than 
1,800,000,000 of miles, and its dimensions such that out of it might be 
formed more than eighty worlds as large as the earth. 

This great discovery excited the highest interest in the astronomical 
world. From the earliest ages, the mighty orbit of Saturn had been re- 
garded as forming the boundary of the vast scheme of planets dependent 
on the sun. Its slow and majestic motion, its great period and distance, 
and the wonderful magnificence of its rings and moons, seemed to render 
it a fitting object to guard the frontiers of the mighty system with which 
it was associated. But the supremacy of Saturn was now gone forever, 
and its sentinel position was usurped by Uranus, whose grand orbit ex- 
panded to twice their original dimensions the boundaries of the solar sys- 
tem. Far sweeping in the depths of space, this new world pursued its 
solemn journey, flinging back the light of its parent orb, steadily obedient 
to the great law of universal gravitation, which held the old planets true 
to their changing orbits. 

Another unit in the number of interplanetary spaces was thus given, 
and the law which might possibly regulate the distances of the planets 
from the sun was sought after with an interest and perseverance which 
could not long fail of its reward. No exact progression was indeed discov- 
ered, but the following remarkable empirical law was detected by Prof. 
Bode : 

Write the series 3 6 12 24 48 96 192, &c. 
Acid to each term 4444 4 4 4 4 

The sums are 4 7 10 16-28 52 100 196. 

Now if 10 be assumed as the earth's distance from the sun, the other 



THE DISCOVERY OF NEW PLANETS. Ill 

terms of tbe series will represent very nearly the distances of the planets 
thus s 

4 7 10 16 28 52 100 196 

Mercury, Venus, Earth, Mars, — , Jupiter, Saturn, Uranus. The fifth term 
in the series is blank, and falls exactly in the enormous interval which exists 
between the orbits of Mars and Jupiter, precisely where Kepler had pre- 
dicted a new planet would be found. As early as 1784, three years after 
the discovery of Uranus, Baron de Zach, struck with the remarkable law 
of Bode, even went so far as to compute the probable distance and period 
of the now generally suspected planet. The impression that a new world 
would be soon be added to the system grew deeper and stronger in the 
minds of astronomers, until finally, in 1800, at a meeting held at Lilienthal, 
by six distinguished observers, the subject was discussed with deep earn- 
estness, and it was finally resolved that the long suspected, but yet, un- 
discovered world, should be made the object of strict and persevering re- 
search. The range of the Zodiac was divided into twenty-four parts, and 
distributed among an equal number of observers, whose duty it was to 
scrutinize their particular regions, and detect, if possible, any moving body 
which might show itself among the fixed stars. 

In case it were possible to note down, with perfect precision, the rel- 
ative places and magnitude of all the stars in a given region, any sub- 
sequent changes which might occur would be easily recognized. In other 
language, could a daguerreotype picture of any region in the heavens be 
made to-night, and at the end of a year another picture of the same re- 
gion could be taken, by comparing the number of stars in the one picture 
with that in the second, in case any one had wandered away from its place, 
or a stranger had come to occupy a place within the limits of the pictured 
region, it would be an easy matter to ascertain either the lost star, or the 
newly arrived stranger. Now, although a daguerreotype picture cannot 
be nad, yet by observation, the exact relative positions of all the visible 
stars may be mapped out, and a picture formed, which shall become the 
ready means of detecting future changes. 

Such was the method of examination adopted by the congress of as- 
tronomers assembled at Lilienthal, in 1800. The organization was made. 
— Baron de Zach was elected president, and Schroeter was chosen per- 
petual secretary. To those who have paid but little attention to the cir- 
cumstances under which this strange enterprise was undertaken, nothing 
can appear more wild and chimerical. To commence a prolonged research 
for an invisible world, one that no keenness of vision could detect, and 
which never could be revealed but by telescopic aid, a world whose 
magnitude was so small that it would not appear so large as a star of the 
smallest size visible to the naked eye, and one which must be sought out 
and detected not by its planetary disk, but by its wanderings among 
thousands of stars, which it in all respects resembled, and from which it 



112 UGTURE OF THE UNIVERSE. 

could in no wise be distinguished, but by its motion, seemed like a wasting 
of time and utter throwing away of labor and energy. 

Piazzi, of Palermo, in Sicily, was one of the planet searching association, 
He had already distinguished himself as an eminent and accurate observer 
and had with indefatigable zeal constructed a most extensive catalogue of 
the relative places of the fixed stars, and thus, in some sense, anticipated 
a part of the labor that the research for the suspected planet contemplated. 
Assisted by his own and by preceding catalogues, he entered on the great 
work with the energy and zeal which distinguished all his great astronomi- 
cal efforts. On the evening of the first day of the year 1801, this as- 
tronomer had his attention attracted by a small star in the constellation 
of the Bull, which he took to be one recorded in the catalogue of Mayer ; 
but on examination, it was found not to occupy any place either on Mayer's 
or his own catalogue. Yet it was so small that it was an easy matter to 
account for this fact, by its having been overlooked in preceding ex- 
plorations of the region in which it was found. With intense anxiety the 
astronomer awaiting the evening of the following night, to settle the 
great question whether the newly detected star was a fixed or moving 
body. On the evening of the 2d of January he repaired to his observatory, 
and so soon as the fading twilight permitted, directed the telescope to the 
exact point in which, on the preceding evening, his suspicious star had 
been located. The spot was blank ! But another, which was distant 4' 
in right ascension, and 3i in declination, which, on the previous night had 
certainly been vacant, was now gleaming with the bright little object 
which, on the preceding evening, had so earnestly fixed his attention, and 
for which he was again so anxiously seeking. Night after night he 
watched its retrograde motion, — a motion precisely such as it ought to 
have, in case it were the long desired planet, — until, on the 12th, it be- 
came stationary, and then slowly commenced progressing in the order of 
the signs. Piazzi was unfortunately taken ill ; his observations were sus- 
pended, and such was the difficulty of intercommunication, that, although 
he sent intelligence of his discovery to Bode and Orani, associates in the 
great enterprise, the newly discovered body was already lost in the rays 
of the sun, before it became possible to renew the train of observations 
by which its orbit might be made known. Piazzi feared to announce the 
newly discovered body to be the suspected planet. His observations were 
few, and he was the only person in the world who had seen it. Bode no 
sooner received the intelligence of its discovery, than he at once pronounc- 
ed it to be the long sought planet, and from the scanty materials furnished 
by Piazzi, Olbers, Burkhart, and Gauss, all computed the elements of its 
orbits, settled the great fact that it was a superior planet, and that its 
orbit was included between those of Mars and Jupiter. Some doubt, 
however, yet rested on the subject, and the disengagement of the planet 
from the beams of the sun was awaited with the deepest interest. 



TEE DISCOVERY OF NEW PLANETS. 113 

Several months passed away. Every eye and every telescope was di- 
rected to the region in the heavens where the new planet was expected to 
be found. The most scrutinizing search was made for its rediscovery, but 
without any success. But for the high reputation of Piazzi, his wel- 
known accuracy and honesty, doubts would have arisen as to whether he 
had not been self-deceived, or was intentionally deceiving others. The 
subject became of deeper and deeper interest. The world began to sneer 
at a science which could find a body in the heavens, and when forever lose 
it. We must remember that Piazzi had followed it through only about 4° 
out of 360° of its orbit, and on this narrow basis a research was to be in- 
stituted, having for its object the determination of the exact position which 
the lost planet must occupy. Gauss, then comparatively a young man, 
and little known as a computer, had conceived a new method of deter- 
mining the orbits of comets, from a very few and very closely consecutive 
observations. Here was an admirable opportunity of giving a practical 
proof of the power of his new method. The long and intricate calculation 
was finished, the place of the lost planet determined, the telescope was 
directed to the spot, and lo ! the beautiful little orb flashed once more on 
the eager gaze of the youthful astronomer. For one entire year had the 
planet been sought in vain, and but for the powerful analysis of Gauss, 
nothing but years of persevering toil could have wiped away the reproach 
which rested on astronomy. 

A sufficent number of observations were soon made to reveal the 
orbitual elements of the planet, now named Ceres. It was found, in all 
respects, to harmonize in its movements with the older planets, and its 
orbit filled precisely the blank in the strange empirical law discovered 
by Bode. The period and distance hypothetically computed from that 
law sixteen years before, by Baron de Zach, were verified in the most re- 
markable manner by the actual period and distance of Ceres. Order and 
beauty now reigned in the planetary system, and a most signal victory 
had crowned the efforts of astronomical science. 

The only remarkable difference betwen the new planet and the old ones, 
consisted in its minute size, the great obliquity of its orbit, and the dense 
atmosphere by which it appears to be surrounded. Its diameter is so 
small as to render its measure next to impossible, and the best practical 
astronomers differ widely in their results. Sir William Herschel makes 
its diameter only 163 miles, while Schroeter cannot make it less than ten 
times that quantity. The mean of these two extremes is probably near 
the truth. — No satellites have been found in attendance on this minute 
planet, although Sir William Herschel suspected the existence of two at 
one time, a suspicion which subsequent observations have not confirmed. 

The beautiful order established in the solar system by the discovery of 
Ceres was a subject of the highest gratification to the whole astronomical 
world, and especially to those who had been instrumental in reaching this 

8 



114 STRUCTURE OF THE UNIVERSE. 

remarkable result. An opportunity had scarcely presented itself for the 
expression of delight occasioned by this announcement, before all interested 
were startled by a declaration from Dr. Olbers, of Bremen, that he had 
found another planet on the evening of the 28th of March, 1802, with a 
mean distance and periodic time almost identical with those of Ceres. This 
discovery broke through all the analogies of the solar system, and presented 
the wonderful anomaly of two planets revolving in such close proximity, 
that their orbits, projected on the plane of the ecliptic, actually intersected 
each other. 

The new planet was called Pallas, and is of a magnitude about equal 
to that of Ceres. Its orbit is greatly inclined to the plane of the ecliptic, 
and its eccentricity is very considerable. The existence of these small 
planets, in such near proximity, for a long while perplexed astronomers. 
At length Olbers suggested that these minute bodies might be the frag- 
ments of a great world, rent asunder by some internal convulsion of suffi- 
cient power to produce the terrific result, but of a nature entirely beyond 
the boundary of conjecture. 

Extraordinary as this hypothesis may appear, the results to which it led 
are not less remarkable. If a world of large size had been actually burst 
into fragments, it is easy to perceive that these fragments, all darting 
away in the orbits clue to their impulsive forces would start from the same 
point, and hence would return at different intervals indeed, but would all 
again pass through the point of space occupied by the parent orb when 
the convulsion occurred. Having found two of these fragmentary worlds, 
the point of intersection of their orbits would indicate the region through 
which the other fragments might be expected to pass, and in which they 
might possible be discovered. So reasonable did the views of Olbers appear, 
that his suggestions were immediately acted upon by himself and several 
distinguished observers, and on the 2d of September, 1804, Mr. Harding, 
of Lilienthal, while scrutinizing the very region indicated by Olbers, de- 
tected a star of the eighth magnitude, which seemed to be a stranger, and 
was soon recognized to be another small planet, fully agreeing, in all its 
essential characteristics, with the theory of Olbers. The new world was 
named Juno, and is remarkable for the eccentricity of its orbit. Its diame- 
ter has not been well determined, owing to its minute size. This dis- 
covery gave to the theory of Olbers the air of reality, and rinding the 
nodes of the three fragments to lie in the opposite constellations Cetus and 
Virgo, he prosecuted his researches in these regions with redoubled energy 
and zeal. 

His efforts were not long without their reward. On the 29th of March, 
1807, he detected the fourth of his fragments in the constellation Virgo, and 
very near the point through which he had, for four years, been waiting to see 
it pass. This was a most wonderful discovery, and almost fixed the stamp of 
truth upon the most extraordinary theory which had ever been promulgated, 



THE DISCOVERY OF NEW PLANETS. 115 

This Dew asteroid was named Vesta, and for nearly forty years the ex- 
aminations which were conducted revealed no new fragment, and it be- 
gan to be regarded as positively ascertained, that all the small bodies re- 
volving in this region had been revealed to the eye. 

But on the 8th day of Dec, 1845, Mr. Hencke, of Dreisen announced to the 
world the discovery of another asteriod, which was named Astrea. Before 
two years had rolled round, the same indefatigable observer discovered a 
sixth member in this wonderful group, which was called Hebe. His suc- 
cess induced other observers to undertake a similar examination, and in a 
very short time the researches of Mr. Hinds of London, were rewarded by 
the discovery of a seventh and eighth asteroid, which were named Iris and 
Flora. 

Thus have we no less than eight of these minute worlds, revolving in 
orbits so nearly aqual, that for weeks and months these miniature orbs 
may sweep along in space, almost within hail of each other. Let us now 
return to an examination of the hypothesis of Olbers, that these are the 
fragments of a world of large size, which once occupied an orbit inter- 
mediate between those of Mars and Jupiter. 

If any internal convulsion could burst a world and separate its fragments, 
it is readily seen that the fragments of largest mass would move in orbits 
more nearly coincident with that of the original planet, while the smaller 
fragments would revolve in orbits greatly inclined to the primitive one. 
This condition is wonderfully fulfilled among the asteroids. The larger 
planets, Ceres and Vesta, revolve in orbits with small inclinations to the 
ecliptic, while the smaller objects are in some instances found to move in 
planes with very great inclinations. The force necessary to burst a planet, 
and to give to its fragments certain orbits, has been computed by Lagrange, 
and he finds that in case any fragment is projected with an initial velocity 
one hundred and twenty-one times greater than that of a cannon ball, it 
would become a direct comet, with a parabolic orbit, while a primitive 
velocity one hundred and fifty-six times greater than that of a cannon ball 
would cause the fragments to revolve with a retrograde motion in the 
curve of a parabola. Any less powerful force would cause the fragment 
to revolve in ellipses ; and it is probable that the force which operated to 
produce the asteroids was not more than twenty or thirty times greater 
than that of a cannon ball. Although the theory of Olbers has received 
new accessions of strength from the discovery of every new asteroid, it 
would be wrong to regard it as one of the demonstrated truths of as- 
tronomy. In the mean time, powerful efforts are making to sour the 
heavens, and a method of observation has been proffered to the Acad- 
emy of sciences, of Paris, by all the visible fragments may be discovered 
within a period of four years. Should this plan, which contemplates a 
division of the heavens among different astronomers, be adopted, volunteers 
have already presented themselves, and the most interesting results maj* 
be anticipated. 



116 STRUCTURE OF THE UNIVERSE. 

From this curious branch of astronomical inquiry we turn to one of still 
deeper interest. In the examinations for new planets, thus far, the tele- 
scope has been the sole instrument of research. Conjectures based upon 
analogical reasoning, it is true, guided the instrumental examinations, but 
the mind had never dared to rise to the effort of reasoning its way analy- 
tically to to exact position of an unknown body. It has been reserved for 
our own day to produce the most remarkable and the boldest theorizing 
which has ever marked the career of astronomical science. — I refer to the 
analytic effort to trace out the orbit, define the distance, and weigh the 
mass of an unknown planet as far beyond the extremest known planet as 
it is from the sun. 

I am fully aware of the difficulties by which I am surrounded, when I 
invite your attention to this complex and intricate subject ; and I know 
how utterly impossible it i, , in a popular effort, to do any kind of justice 
to the intricate and involved reasoning of the great geometers, who have 
not only rendered themselves, but the age in which we live, illustrious by 
their efforts to resolve this, the grandest problem which has ever been 
presented for human genius. — Trusting to your close attention, I shall 
attempt to exhibit some faint outline of the train of reasoning and the kind 
of research employed in rescuing an unknown world from the viewless 
regions of space in which it has been tracing its unknown orbit for ages 
commensurate with the existence of the great system of orbs of which it 
constitutes a part. 

After the discovery of the planet Uranus, by Sir William Herschel, 
geometers were not long in fitting it with an orbit which represented in 
the outset, with accuracy, its early movements. With this orbit it became 
possible to trace its career backwards, and to define its position among the 
fixed stars for fifty or one hundred years previous to the date of its dis- 
covery. This was actually done, with the hope of finding that the place 
of the planet had been observed and recorded by some astronomer, who 
ranked it among the fixed stars. This hope was not disappointed. The 
planet, believed to be a fixed star, had been seen and observed no less than 
nineteen different times, by four different observers, through a period run- 
ning back nearly one hundred years previous to the discovery of its plan- 
etary character by Herschel. These remote observations were of the great- 
est value as data for the determination of the elements of its elliptic orbit, 
and for the computation of the mean places, which might serve to predict 
its position in coming years. 

A distinguished astronomer, M. Bouvard, of the Paris Academy of 
Sciences, about thirty years ago, undertook the analytic investigation of 
the movements of Uranus, and a computation of exact tables. He was met, 
however, by difficulties which, in the state of knowledge as it then existed, 
with reference to this planet, were absolutely insurmountable. He found 
it quite impossible to obtain any orbit which would pass through the places 



THE DISCOVERY OF NEW PLANETS. 11? 

of the planet determined after its discovery, and through those positions 
which had been fixed previous to that epoch. In this dilemma it became 
necessary to reject the old observations as less reliable than the new ones, 
and the learned computer leaves the problem for posterity to resolve, 
carefully abstaining from any absolute decision in the case. 

His orbit, based upon the new or modern observations, and his tables 
being computed, it was hoped that the theoretic places of the planet would 
thereafter coincide with the observed places and that all discrepancies 
which might not be fairly chargeable to errors of observation, would be re- 
moved. In this expectation, however, the astronomical world was dis- 
appointed ; and while the tables of Bouvard failed absolutely to represent 
the ancient observations, in a few years they were but little more truthful 
in giving the positions actually filled by the planet under the telescope. 
The discrepancies between the theoretic and actual places of the planet 
began to attract attention many years since. As early as 1838, Mr. Airy, 
Astronomer Royal of England, on a comparison of his own observations 
with the tables, found that the planet was out of its computed track, by a 
distance as great as the moon's distance from the earth, and that it was act- 
ually describing an orbit greater than that pointed out by theory. It seemed 
that this remote body was breaking away from the sun's control, or that it 
was operated on by some unknown body deep sunk in space, and which 
thus far had escaped the scrutinizing gaze of man. 

These deviations became so palpable as to attract general attention, and 
various conjectures were made with reference to their probable cause. 
Some were disposed to regard the law of gravitation as somewhat relaxed 
in its rigorous application to this remote body ; others thought the devia- 
tion attributable to the action of some large comet, which might sway the 
planet from its course ; while a third set of philosophers conjectured the 
existence of a large satellite revolving about Uranus, and from whose at- 
traction the planet was caused to swerve from the computed orbit. These 
conjectures were not sustained by any show of reasoning, and were of no 
scientific value. 

Such was the condition of the problem when it was undertaken by a 
young French astronomer, not quite unknown to fame in his own country, 
but comparatively at the beginning of his scientific career. The friend of 
Arago, Leverrier's Cometary Investigations, and more especially his re- 
searches of the motions of Mercury, had gained for him the confidence of 
this distinguished savant, and Arago urged on his young associate the im- 
portance of the great problem presented in the perturbations of Uranus, 
and induced him to abandon other investigations, and concentrate all the 
energies of his genius on this profound and complex investigation. 

The extraordinary powers of Leverrier as a mathematical astronomer 
had been so successfully displayed in his researches of the motions of 
Mercury, that it deserves a passing notice. The old tables of this planet, 



11$ srnrcrcnE of the exit ex se. 

Leverrier believed to be defective. He therefore set about a thorough ex- 
amination of its entire theory, and after a rigid scrutiny, deduced a new 
set of tables, from which the places of the planet might be predicted with 
greater precision. 

The transit of Mercury across the sun's disc, which occurred on the 8th 
day of May, 1845, presented an admirable opportunity to test the truth of 
the new theory of the young astronomer. Most unhappily for his hopes, 
all observations in Paris were rendered impossible by the clouds, Avhich 
covered the heavens during the entire day on which the transit took place. 
While the computer was sadly disappointed, I was more fortunate, for a 
pure and transparent atmosphere favored this, the first astronomical ob- 
servation I ever made. A slight reference to this occurrence may be par- 
doned. For three years I had been toiling to complete a most difficult and 
laborious enterprise, the erection of an astronomical observatory of the first 
class, in a country where none had ever existed. Amid difficulties and 
perplexities which none can ever know, the work bad moved on, and at 
length I had the high satisfaction of seeing mounted one of the largest and 
most perfect instruments in the world. I had arranged and adjusted its 
complex machine^ — had computed the exact point on the sun's disc where 
the planet ought to make its first contact — had determined the instant of 
contact by the old tables, and by the new ones of Leverrier, and with feel- 
ings which must be experienced to be realized, five minutes before the com- 
puted time of contact, I took my post at the telescope to watch the coming 
of the expected planet. After waiting what seemed almost an age, I called 
to my friend how much time was yet to pass, and found but one single 
minute out of five had rolled heavily away. The watch was again resumed. 
Long and patiently did I hold my place, but again was forced to call out, 
how speeds the time ? and was answered that there was yet wanting two 
minutes of the computed time of contact. — With steadfast eye, and a throb- 
bing heart, the vigil was resumed, and after waiting what seemed an age, 
I caught the dark break which the black body of the planet made on the 
bright disc of the sun. Now! I exclaimed; and within sixteen seconds 
of the computed time did the planet touch the solar disc, at the precise 
point at which theory had indicated the first contact would occur. 

The planet was followed across the disc of the sun, round and sharp, and 
black, and every observation confirmed the superior accuracy of the new 
tables of Leverrier. While the old tables were out fully a minute and a 
half in the various contacts, those of Leverrier were in error by only about 
sixteen seconds as a mean. 

The great success of this investigation encouraged the young astronomer 
to accept the difficult task which Arago proposed for his accomplishment, 
and he earnestly set about preparing the way for a full discussion of the 
grand problem of the perturbations of Uranus. The importance of the 
subject demanded the greatest caution, and having determined to rely 



THE DISCOVERY OF NEW PLANETS. 119 

solely on his own efforts, he at once rejected all that had been previously 
done, and commenced the problem at the very beginning. New analytic 
theories were formed ; elaborate investigations of the planets Jupiter and 
Saturn, as disturbing bodies, were made, and an entire clearing up of all 
possible causes of disturbance in the known bodies of the system was 
laboriously and successfully accomplished, and the indefatigable mathemati- 
cian finally reached a point where he could say, here are residual perturba- 
tions which are not to be accounted for by any known existing body, and 
their explanation is to be sought beyond the present ascertained limits of 
the solar system. 

As early as the 10th of November, 1845, M. Leverrier presented a 
memoir to the Royal Academy of Sciences in Paris, in which he determined 
the exact perturbations of Jupiter and Saturn on Uranus. This was fol- 
lowed by a memoir, read before the academy on the 1st of June, 1846, in 
which he demonstrates that it is impossible to render an exact account of 
the perturbations of Uranus in airy other way than by admitting the exist- 
ence of a new planet exterior to the orbit of Uranus, and whose heliocen- 
tric longitude he fixes at 325 b on the 1st of January, 1847. On the 30th 
of August, 1846, a third memoir was presented to the academy, in which 
the elements o^ the orbit of the unknown planet are fixed, together with its 
mass and and actual position, with greater accuracy, giving on the 1st of 
January, 1847, 326 6 32' for its heliocentric longitude. Finally, on the 5th 
of October, 1847, a fourtn Jiemoir was read, relative to the determination 
of the plane of the orbit of tho constructive planet. 

It is quite impossible to convey, in popular form, the least idea of the 
profound analytic reasoning employ * d by M. Leverrier in this wonderful 
investigation. None but the rarest genius would have dared to reach out 
1,800,000,000 of miles into unknown regions of space, to feel for a planet 
which had displaced Uranus by an amount only about equal to four times 
the apparent diameter of the planet Jupiter, as seen with the naked eye — 
a quantity so small that no eye, however keen and piercing, without tele- 
scopic aid, could ever have detected it. Yet from this minute basis was 
the magnificent superstructure to be reared which should eventually direct 
the telescope to the place of a new and distant world. To many minds, 
the resolution of such a problem may appear utterly beyond the powers 
of human genius, and without one ray of light to illumine the midnight 
darkness which surrounds it to them, they are disposed to reject the entire 
subject. An attentive examination of the following train of reasoning may 
at least demonstrate that the problem is not quite so hopeless as it would 
at first appear. 

It was not necessary to extend researches to all quarters of the heavens 
indifferently, in an effort to find the unknown body. All the planets re- 
volve in planes nearly coincident with the plane of the earth's orbit, and 
more especially do the distant ones. Jupiter and Saturn and Uranus re» 



120 STRUCTURE OF THE UNIVERSE. 

volve in orbits but little inclined to the plane of the ecliptic. — Hence, it 
was fair to conjecture that the new planet, should it ever be found, would 
not violate this general law, and a search for it was properly limited to a 
narrow belt near the plane of the earth's orbit. — The limits of research 
were thus brought down to a narrow zone, sweeping around the entire 
heavens indeed, but insignificant in extent, when comoared with the whole- 
celestial sphere. 

The next point of examination was the probable distance of the unknown 
planet. Here, again, analogy came to the aid of Leverrier. The empirical 
law of Bode, already explained in a former lecture, showed that the remote 
planets increase their distances by a very simple law. Saturn was twice 
as remote as Jupiter; Uranus was at double the distance of Saturn, and it 
was fair to conclude that the unknown planet would be about twice as far 
from the sun as Uranus. As a first approximation, then, its distance was 
fixed at about 3,600,000,000 of miles from the sun. Kepler's law, regulat- 
ing the ratio between the distances and periods of the planets, gave at once 
the time of revolution of the new planet, in case its distance had been cor- 
rectly assumed. In the next place, it was fair to conclude that the orbit 
of the new planet, like those of Jupiter, Saturn, and Uranus, would not 
differ greatly from a circle. These conjectures were, in some degree, con- 
firmed by a very simple train of reasoning with reference to the distance 
of the disturbing body. If it revolved in an orbit very near to that of 
Uranus, then its effect on Uranus ought to be excessive, when compared 
with its influence on Saturn, which was found not to be the case. Again, 
if it revolved in an orbit very far beyond the limit assigned above, its 
effect on Uranus and Saturn would be very nearly the same, which was not 
verified by examination. 

Having thus roughly fixed limits for the orbit of the unknown body, 
the work of the mathematician now commences, having for its grand object 
the determination of the true places of the planet sought at some given 
epoch, and such an orbit as will represent the perturbations of Uranus in 
the most perfect manner. To exhibit, in some faint degree, the difficulty 
of this investigation, let us conceive that up to the 1st of January, 1800, 
the solar system had consisted only of the known bodies, the sun, planets, 
satellites, and comets. The orbits of all the planets are accurately ascer- 
tained, and their reciprocal influences computed and known. The outer- 
most planet, Uranus, revolves in its vast orbit obedient to the great law of 
gravitation, acknowledging the predominant influence of the sun, and 
swaying more or less to the action of the nearest planets, Saturn and 
Jupiter. Its predicted and observed places coincide, and its movement is 
followed with confidence and exactitude. 

With a full and perfect knowledge of the orbit of Uranus, let a new 
planet be created and projected in a vast orbit exterior to, and remote from 
the orbit of Uranus. The new body thus added to the system would in- 



THE DISCOVERY OF NEW PLANETS. 121 

stantly derange the motions of Uranus, causing it to recede from the sun, 
and increasing its mean period of revolution. In this case, the total effect 
of the new planet on Uranus would be perturbation, and it would not be 
quite impossible, even for one not skilled in the higher mathematics, to see 
how the action of the newly created planet on the movements of the old 
one might actually reveal approximately the position of the disturbing 
body. It is manifest that when the two planets are in conjunction, or on 
a right line passing through them and the sun, that at this configuration 
the new planet would exert its greatest power to drag the old one outward 
from the sun, and if it could be found at what point of its orbit the old 
planet actually receded to its greatest distance from the sun, in the 
same direction, nearly, must the disturbing body have been situated at 
that time. In this way, we perceive, one place of the new planet might 
be approximately found, and from its periodic time it would be possible to 
trace it backward or forward in its orbit, for the present supposed to be 
circular. 

The problem here presented is certainly sufficiently difficult, yet its 
complexity is very far from being equal to that presented in nature, and 
with which the French geometer found himself obliged to grapple. — 
Although unknown, the new planet did exist, and for ages had silently 
pursued its unknown orbit round the sun. Its influence on Uranus had 
been ever active, and when the observations on Uranus were made, and 
its places determined, from which its elliptic elements were to be derived, 
these very places were in part dependent on the action of the invisible 
disturber, and hence a portion of its influence would be darkly concealed 
in the orbit of Uranus ; and to divide the entire effect of the new planet 
on the old one correctly between the disguised portion and that producing 
real perturbation, was attended with the greatest difficulty, and could 
only be reached by adopting certain positive hypotheses. Surrounded by 
all these difficulties, Leverrier worked on, and with consummate art, so 
constructed his analytical machinery as to meet and master every diffi- 
culty ; and he finally announces to the world the figure of the orbit of his 
imaginary planet, its distance, period of revolution, and even the mass of 
matter it contains. 

These important communications were made to the French Academy 
of Sciences, on the 31st of August, 1846. On the 18th of the following 
month, M. Leverrier wrote to his friend M. Galle, of Berlin, requesting 
him to direct his telescope to that point in the heavens which his com- 
putations had revealed as the one occupied by the constructive planet. 
The request was readily complied with, and on the very first evening of 
examination, a star of the eighth magnitude was discovered, which was 
evidently a stranger in that region, as it was not found on an accurate 
map of the heavens including all stars of that magnitude. The following 
evening was awaited with the deepest interest, to decide, by the actual 



122 STRUCTUKE OF THE UKIVERSE. 

motion of the suspected star, whether indeed it was the planet so wonder- 
fully revealed by the analysis of Leverrier. The night came on. Again 
was the telescope directed to the star in question, when lo ! it had moved 
from its former place, in a direction and with a velocity almost precisely 
accordant with the theory of the French geometer ! The triumph was 
perfect — the planet was actually found. The news of its discovery flew 
in every direction, and filled the world with astonishment and admiration. 

The exceeding accuracy with which its place had been predicted, com- 
ing within less than one degree of its actual position, gave to M. Leverrier 
the highest confidence in the, perfection of his analysis, and filled with 
astonishment the oldest and most learned astronomers. If scepticism had 
existed with reference to the possible solution of so complex a problem — 
if the theory of Leverrier had been regarded as a beautiful speculation, 
ingenious and plausible, but vain in its practical application — the actual 
discovery of the planet silenced all cavil, and put to flight every lingering 
doubt. 

As if anything were wanting, to give a more positive character to the 
computations of Leverrier, it was now found that a young English 
mathematician, Mr. Adams, of Cambridge, had actually accomplished the 
resolution of precisely the same problem, and had reached results almost 
identical with those of the French geometer. This astonishing coinci- 
dence on the part of two computers unknown to each other, each starting 
from the same data, pursuing independent trains of reasoning, and arriv- 
ing at the same results, confirmed, as it would seem, in the fullest man- 
ner, the accuracy of the resolution which had been obtained. 

On learning that Leverrier had communicated to the Academy of 
Sciences, in August, 1846, his final results, I wrote immediately request- 
ing the computed place of his planet, with such directions as would best 
guide me in a search which I desired to make for it with the great re- 
fracting telescope of the Cincinnati Observatory. But before my letter 
reached its destination, the planet had been found, and the news of its 
discovery soon reached the United States. It was almost impossible for 
me to credit the statement, and I was almost disposed to believe that the 
prediction of the planet's position had been mistaken for its actual dis- 
covery. With these conflicting doubts, I waited for the coming of night 
with a degree of anxiety and excitement which may be readily imagined. 
I had no star chart to guide me in my search for the planet ; — I had no 
meridian instrument with which to detect it by its motion ; but I was not 
without hope that the power of our great telescope, might be sufficient to 
select, at once, the planet from among the fixed stars, by the magnitude 
of its dish. 

As soon as the twilight disappeared, the instrument was directed to 
the point in the heavens where the planet had been found. I took my 
place at the finder or small telescope attached to the larger one, and my 
assistant was seated at the gre at instr ument. 



THE DISCOVERY OF NEW PLANETS. 123 

On placing my eye to the finder, four stars of the eighth magnitude oc- 
cupied its field. One of them was brought into the field of the large 
telescope, and critically examined by my assistant, and rejected. A second 
star was in like manner examined, and rejected. A third star, rather 
smaller and whiter than either of the others, was now brought to the 
centre of the field of the great telescope, when my assistant exclaimed, 
44 there it is ! there is the planet ! with a disk as round, bright and beauti- 
ful as that of Jupiter ! " There, indeed, was the planet, throwing its 
light back to us from the enormous distance of more than 3,000,000,000 
of miles, and yet so clear and distinct, that in a few minutes, its diameter 
was measured, and its magnitude computed. 

It is not my intention to follow, critically, the history of this wonder- 
ful discovery, yet there are some facts so remarkable that it would be 
wrong to pass them in silence. From the moment the planet was detect- 
ed in Berlin, it has been observed by all the best instruments in the world, 
with a view of ascertaining how accurately theory had assigned the ele- 
ments of its orbit. In consequence of its very slow motion, it became a 
matter of the utmost importance to obtain, if possible, some remote 
observation made by an astronomer who might have entered the place of 
the planet in his catalogue as a fixed star. Mr. Adams, of England, led 
the way in the computation of the elements of the orbit of the new 
planet, from actual observation, and was followed by many other com- 
puters, among them our countryman S. C. Walker, then of the Washington 
Observatory. 

Having obtained an approximate orbit, Mr. Walker computed back- 
wards the places of the new planet for more than fifty years, and then 
examined the late catalogues, in the hope of finding its place on some of 
them as a fixed star. Among recent catalogues there was no success, but 
in an examination of Lalande's catalogue, he found an observation on a 
star of the eighth magnitude, made May the 10th, 1795, which was so 
near the place which his computation assigned the planet at the same 
date, that he was led to suspect that this star might indeed prove to be 
the new planet. In case his conjecture were true, on turning the tele- 
scope to the place occupied by the star, it would be found blank, as its 
planetary motion would have removed it very far from the place which it 
occupied more than fifty years before. The experiment having been 
made, no star could be found, and strong evidence was thus presented 
that Mr. Walker had actually found an observation of the new planet, 
giving its position in 1795 ;' but in consequence of the great discrepancy 
between the period of M. Leverrier and that which would result from a 
reliance on this observation of the new planet Neptune, Mr. Walker's 
discovery was at first received with great hesitation. A greater doubt 
was thrown over the matter from the fact that Lalande had marked the 
observation as uncertain, and it w - only by reference to the original 



124 STRUCTURE OF TBE UNIVERSE. 

manuscripts preserved in the Royal Observatory of Paris that the doubts 
could be removed. 

The discovery of Mr. Walker was subsequently made by Mr. Petersen, 
of Altona, and the results of these astronomers reached Paris on the same 
day. A committee was at once appointed to examine the original man- 
uscript of Lalande, when a most remarkable discovery was made. This 
astronomer had observed a star of the eighth magnitude on the evening 
of the 8th of May, 1795, and on the evening of the 10th, not finding the 
star as laid down, but observing one of the same magnitude very near the 
former place, he rejects the observation of the 8th of May as inacurate, 
and enters the observation of the 10th, marking it doubtful. 

On close examination, this star proves to be the planet Neptune, and 
by this discovery we are placed in possession of observations which render 
it possible to determine the elliptic elements of the new planet with great 
precision. These differ so greatly from those announced by Leverrier and 
Adams previous to the discovery, that Prof. Pierce, of Cambridge, Mass., 
pronounces it impossible so to extend fairly the limits of Leverrier's 
analysis as to embrace the planet Neptune ; and that, although its mass, 
as determined from the elongations of its satellite, renders it possible to 
account for all the perturbations of Uranus by its action, in the most 
surprising manner, yet, in the opinion of Prof. Pierce, it is not the planet 
to which geometrical analysis directed the telescope. Leverrier rejects 
absolutely the result reached by the American geometer, and claims 
Neptune to be the planet of his theory, in the strictest and most legitimate 
sense. 

Time and observation will settle the differences of these distinguished 
geometers, and truth being the grand object of all research, its discovery 
will be hailed with equal enthusiasm by both of the disputants. In any 
event, the profound analytic research of Leverrier is an ever-during 
monument to his genius, and his name is forever associated with the most 
wonderful discovery that ever marked the career of astronomical science. 



LECTURE VIII. 

THE COMETARY WORLDS. 

The wonderful characteristics which mark the flight of comets through 
space ; the suddenness with which they blaze forth ; their exceeding veloc- 
ity, and their terrific appearance ; their eccentric motions, sweeping 
towards the sun from all regions and in all directions, have rendered 
these bodies objects of terror and dread in all ages of the world. While 
the planets pursue an undeviating course round the sun, in orbits nearly 
circular, and almost coincident with the plane of the earth's orbit, all 
revolving harmoniously in the same direction, the comets perform their 
revolutions in orbits of every possible eccentricity, confined to no particu- 
lar plane, and moving indifferently in accordance with, or opposed to, the 
general motion of the planets. They come up from below the plane of 
the ecliptic, or plunge downwards towards the sun from above, sweep 
swiftly round this their great centre, and with incredible velocity wing 
their flight far into the fathomless regions of space, in some cases never 
again to reappear to human vision. 

In the early ages of the world, superstition regarded these wandering 
fiery worlds with awe, and looked upon them as omens of pestilence and 
war ; and indeed, even in modern times, no eye can look upon the fiery 
train spread out for millions of miles athwart the sky, and watch the 
eccentric motions of these anomalous objects, without a feeling of dread. 
The movements of the planets inspire confidence. They are ever visible, 
and true to their appointed times while the comet, erratic in its course, 
bursts suddenly and unannounced upon the sight, and no science can pre- 
dict in the outset its uncertain track — whether it may plunge into the 
sun, or dash against one of the planetary systems, or even come into collis- 
ion with our own earth, is equally uncertain, until after a sufficient num- 
ber of observations shall have been made to render the computation of 
the elements of its orbit possible. 

Previous to the discovery of the law of universal gravitation, comets 
were looked upon as anomalous bodies, of whose motions it was quite 
impossible to take any account. By some philosophers they were regard- 
ed as meteors kindled into a blaze in the earth's atmosphere, and when 
once extinguished they were lost forever. Others looked upon them as 
permanent bodies, revolving in orbits far above the moon, and reappear- 
ing at the end of long but certain intervals. When, however, it was dis- 



126 STRUCTURE OF THE UNIVERSE. 

covered that, under the influence of gravitation, any revolving world 
might describe either of the four curves, the circle, ellipse, parabola or 
hyperbola, it at once became manifest that the eccentric movements of the 
comets might be perfectly represented by giving to them orbits of the 
parabolic or hyperbolic form, the sun being located in the focus of the 
curve. According to this theory, the comet would become visible in its 
approach to its perihelion, or nearest distance from the sun, — would here 
blaze with uncommon splendor, and in its recess to the remote parts of its 
orbit, would gradually fade from the sight, relaxing its speed, and perform- 
ing a large prouortion of its vast curve far beyond the reach of human 
vision. 

Such was the theory of Newton, and such were the fair deductions 
from the great law of nature which he had revealed to the world. He 
awaited with deep interest the appearance of some brilliant comet, whose 
career he might trace, in the full confidence that observation would con- 
firm the truth of his bold hypothesis. Fortunately, his impatience was 
soon gratified. In the year 1680 a most wonderful comet made its ap- 
pearance, which, by its splendor and swiftness, excited the deepest inter- 
est throughout the world. It came from the regions of space immediately 
above the ecliptic, and plunging downwards with amazing velocity, in a 
direction almost perpendicular to this plane, it appeared to direct its flight 
in such manner that it must inevitably plunge directly into the sun. This 
was not, however, the case. Increasing its velocity as it approached the 
sun, it swept round this body with the speed of a million of miles an hour, 
approaching the sun to within a distance of its surface of a sixth part of 
the sun's radius. It then commenced its recess, throwing off a train of 
light which extended to the enormous distance of 100,000,000 of miles. 
With the swiftness of thought almost, it swept away from the sun, and 
was gradually lost in the distant regions of space whence it came, and has 
never since been seen. Such were the general characteristics of the body 
to whose rapid motions Newton attempted to apply the law of universal 
gravitation. 

Its positions were marked with all the accuracy which the instruments 
then in use permitted, and it was found that a parabolic curve could be 
constructed which would embrace all the places of the comet. — The great 
eccentricity of its orbit, and its vast period, amounting to nearly six hun- 
dred years, gave to the comet great interest, but rendered it an unfit ob- 
ject for successful analytic research. The great English astronomer, 
Halley, had studied it with the closest care, and with a rigid application 
of Newton's theory, he reached results quite as satisfactory as the circum- 
stances of the case rendered possible. 

Fortunately, in 1682, another comet made its appearance, to the study 
of which Halley devoted himself with a zeal and success which has justly 
stamped his name on this remarkable body ; and as our limits forbid an 



THE COMET ARY WORLD. 127 

extensive investigation of the history and theory of comets, I propose to 
examine this one with that degree of detail which may convey some idea 
of the limits of human knowledge in this complicated department of 
science. 

At the suggestion of Newton, Halley had searched all ancient and 
modern records, for the purpose of rescuing any historical details touch- 
ing the appearance and aspect of comets, from the primitive ages down 
to his own time. On the appearance of the comet of 1682, he observed 
its position with great care, and with wonderful pains computed the 
elements of its orbit. . He found it moving in a plane but little inclined 
to the ecliptic, and in an ellipse of very great elongation. In its ophelion, it 
receded from the sun to the enormous distance of 3,400,000,000 of miles. — 
He discovered that the nature of its orbit was such as to warrant the 
belief that the comet would return at regular intervals of about seventy- 
five years, and recurring to his historical table of comets, he found it 
possible to trace it back with certainty several hundred years, and with 
probability even to the time of the birth of Mithridates, one hundred and 
thirty years before Christ. At this, its first recorded appearance, its magni- 
tude must have been far beyond anything subsequently seen, as its 
splendor is said, to have surpassed that of the sun. 

In the years 248, 324, and 399 of the Christian era, remarkable comets 
are recorded to have appeared, and the equality of interval corresponds 
well with Halley's comet. In the year 1006, it presented a frightful as- 
pect, exhibiting an immense curved tail in the form of a scythe. In 1456, 
its appearance spread consternation through all Europe, and led to most 
extravagant acts on the part of the reigning pontiff, who actually insti- 
tuted a form of prayer against the baleful influence of the comet, and 
thus increased the terrors of the ignorant and superstitious. The comet 
appeared with certaint}^ in 1531, and again in 1607, and from an exami- 
nation of all the facts, and with full confidence in his computations, Halley 
ventured the bold prediction that this same comet would reappear about 
the close of 1758, or the beginning of 1759» 

This was certainly the most extraordinary prediction ever made, and 
the distinguished philosopher, knowing that he could not live to witness 
the verification of this prophetic announcement, expresses the hope that 
when the comet shall return, true to his computed period, posterity will 
do him the justice to remember that this first prediction was made by an 
Englishman. In the age when these investigations were made, the theory 
of comets was in its infancy, and it is believed by those competent to 
form a just opinion, that Halley was the only man living who could have 
computed the orbit of his comet. 

As the period approached for the verification of this extraordinary an- 
nouncement, the greatest interest was manifested among astronomers, and 
efforts were made to predict its coming with greater accuracy, by com- 



128 STRUCTURE OF THE UNIVERSE, 

puting the disturbing effects of the larger planets within the sphere of 
whose influence the comet might pass. This was a new and difficult 
branch of astronomical science, and it would be impossible to convey the 
least idea of the enormous labor which was gone through by Clairaut and 
Lalande, in computing the perturbations of this comet through a period 
of two revolutions, or one hundred and fifty years. 

" During six months," says Lalande, " we calculated from morning till 
night, sometimes even at meals, — the consequence of which was that I 
contracted an illness which changed my constitution during the remainder 
of my life. The assistance rendered by Madame Lepaute was such, that 
without her we never should have dared to undertake the enormous labor, 
in which it was necessary to calculate the distance of each of the two 
planets, Jupiter and Saturn, from the comet, separately for every degree, 
for one hundred and fifty years. 

Amid all these difficulties, the computers toiled on until finally, the 
period coming on rapidly for the comet's return, they were forced to 
neglect some minor irregularities, and Clairaut announced that the comet 
would be retarded one hundred days by the influence of Saturn, and five 
hundred and eighteen days by the action of Jupiter ; — he therefore fixed 
its perihelion passage for the 13th of April, 1759, stating, at the same 
time, that the result might be inaccurate by some thirty days either way, 
in consequence of being j^ressed for time, and his having neglected cer- 
tain small perturbations. 

These results were presented to the Academy of Sciences on the 14th 
of November, 1758, and on the 25th of the following December, George 
Palitch, an amateur peasant astronomer, caught the first glimpse of the 
long expected wanderer, which, after an absence of three-quarters of a 
century, once more returned to crown with triumph the great English 
astronomer who first foretold its period, and the eminent French mathe- 
maticians who had actually computed its perihelion passage, to within nine- 
teen days, in seventy-six years ! 

Here, then, was a new world added to the solar system, linked to the 
sun by the immutable law of gravitation ; sweeping out into space to the 
amazing distance of 8,800,000,000 of miles ; lost to the gaze of the most 
powerful telescope, and yet traced by the human mind through its vast 
and hidden career, with an accurac}^ and precision from which there was 
no escape. The very small error of nineteen days in Clairaut's compu- 
tation strikes us with astonishment, when we remember the imperfect 
state of analytical science at that day, and the fact that two planets 
Uranus and Neptune, which have since been discovered, were then not 
even suspected to have any existence. 

The magnificent display which had marked some of the early returns 
of Halley's comet, and which produced such consternation among all 
classes, the educated as well as the ignorant, were not presented during 



THE COMETARYWORLDH 1129 

its appearance in 1758. This was owing," in part, to"' the unfavorable 
position of the earth in its orbit at the time of the comet's perihelion 
passage. — The vast trains of light which are sometimes seen to accompany 
comets, are only displayed in their approach to the sun. They attain 
their greatest splendor while the comet is in the act of passing its peri- 
helion, and as it recedes into space, the tail fades away, from two causes 
— an actual diminution from condensation, and an apparent decrease on 
account of increased distance. 

As the comet, when near the sun, moves with increased velocity, it 
occupies, in general, only a short period in passing through the limits of 
distance from the sun within which any train of light is developed. It 
may happen that at one return of the same comet, the earth may occupy 
a point in her orbit, during its perihelion passage, which may be very 
near to the comet, and thus afford an opportunity of witnessing its ap- 
pearance at a short distance ; while, on the next return, the earth being 
at a remote part of its orbit while the comet is passing the sun, it may be 
seen only with great difficulty, or even become quite invisible. If, there- 
fore, astronomers were obliged to depend upon a uniform physical appear- 
ance of comets at their successive returns, to determine their identity, 
there would scarcely be the slightest chance of ever recognizing even a 
single one among the many thousands which are sweeping through the 
regions of space. 

The interval from 1759 to 1835, when Halley's comet ought to make 
its next appearance, had witnessed extraordinary changes in astronomy. 
The methods for computing planetary perturbations had been greatly 
improved ; the planet Uranus had been added to the system, and more 
accurate masses of the larger planets, especially of Saturn, had been ob- 
tained. Twenty-five years before the close of the comet's period, its 
return commenced to interest astronomers, and prizes were offered by 
two academies for the most perfect theory of this remarkable body. 
Baron Damoiseau and M. Pontecoulant were the successful competitors 
for the two prizes, although several other astronomers undertook and 
completed the task of computing the planetary perturbations. Although 
the computers differed slightly in the time of the perihelion passage, the 
difference was clue to the imperfection of the data employed, rather than 
to any defect in the methods of computation. 

For the expected return in 1835, not only was the perihelion passage 
computed, but the exact route of the comet among the fixed stars was 
wrought out with surprising accuracy, and the precise point towards 
which the telescope must be directed at the time when the comet would 
first attain the limits of visibility. Strange and almost incredible as it 
must appear, guided by these predictions, M. Dumouchel, director of the 
observatory of the Roman College, on the evening of the 5th of August, 
1835, fixed his telescope in the position indicated by computation, and, 

9 



130 STRUCTURE OF THE UNIVERSE. 

on placing his eye to the tube, lo ! the comet appeared, as a faint and 
almost invisible stain of light on the deep blue of the heavens. 

Again did science triumph, in the most remarkable manner, and the 
computed orbit of the comet was followed by it with the most surprising 
accuracy. — The perihelion passage was predicted to within nine days of 
its actual occurrence, a most astonishing approximation to the truth, when 
it is remembered that this body, far as it penetrates into space, never, 
even at the remotest point of its orbit, escapes from the sensible influence 
of the planet Jupiter. Moreover, at that time, the new planet, Neptune, 
was unknown, and its influence over the comet could not be taken into 
account. 

It is interesting to remark the confidence with which astronomers 
relied on Halley's comet for information relative to those bodies, which 
inhabited the regions of space exterior to the known limits of the solar 
system. It was urged by every computer that the orbit of this comet 
would one day come to be so perfectly known, that the perturbations 
due to the recognized bodies of the solar system might be computed 
with such precision, that the residual perturbations might be pronounced 
to be the effect of unknown planets or comets circulating in the distant 
regions of space. This conjecture has been realized, although by dif- 
ferent means, and a planet is now added to our s} r stem which revolves in 
an orbit so vast as to circumscribe within its limits the entire sweep of 
the comet; and as the orbits of Neptune and Halley's comet are inclined 
under an angle only of 15° or 16°, a time will come when the perturbations 
experienced by the comet when at its aphelion, from Neptune's influence, 
may be so great that, but for the fortunate discovery of the cause, would 
have falsified, in the most unaccountable manner, the predictions of the 
comet's return by future astronomers. During its late return, the finest 
telescopes in the world were employed in a critical examination of the phys- 
ical condition of Halley's comet. Elaborate drawings have been made by 
M. Struve, the distinguished director of the Imperial Observatory at 
Pulkova, Russia, with the grand refracting telescope under his charge, 
and also by Sir John Herschel, at the Cape of Good Hope, with a twenty 
feet reflector of superior power. To these beautiful drawings reference 
will be made hereafter. 

The most wonderful changes in the magnitude and figure of the comet 
were observed to take place from night to night, and almost perceptible 
from hour to hour under the eye of the observer. The nucleus was 
sometimes seen sharp and strongly condensed, with more or less nebulous 
light around it. Sometimes a luminous crescent became distinctly visible 
near the nucleus, giving to the comet a most extraordinary appearance. 
At one time M. Struve saw the comet attended by two delicately shaped 
appendages of light of a most graceful form, the one preceding, the other 
following the nucleus of the comet. At other times it was seen to be 



THE COMET ARY WOULD. ■ 131 

surrounded by a sort of semi-circular veil, which, extending backwards, 
was lost in a double train of light, which flung itself out to a vast 
distance from the body of the comet. 

Leaving, for the present, the consideration of the physical constitution 
of these eccentric bodies, we proceed to the examination of a remarkable 
object which bears the name of Encke's comet, in consequence of the 
discovery by this learned astronomer that its orbit was elliptical, and its 
period of revolution so short as to fall fairly within the limits of perpetual 
examination. 

In 1818, a comet was discovered by Pons, not at all remarkable for 
its magnitude, for it was even invisible to the naked eye, but when the 
attempt was made to represent its places by a parabolic orbit, which 
had thus far been invariably applied to the comets, it was found impossible 
to assign any elongated orbit which would embrace the observed positions 
of the comet. After a very elaborate 'investigation, Professer Encke at 
length reached the conclusion that the orbit was not a parabola, but an 
ellipse of comparatively small dimensions, and that this comet was act- 
ually revolving around the sun in a period of about three years. This 
discovery excited a great deal of interest, for it was the first in which a 
short period had been detected, and efforts were at once made to identify 
the new member of the solar system in its preceding revolutions. 
Olbers determined its identity with a comet which appeared in 1795, 
and subsequently ascertained that another, which had been observed but 
twice in 1786, and from which observations no elements could be computed 
could be no other than the new comet of that period. In this way, observa- 
tions on this interesting object were obtained, stretching through some 
thirty-three years, or about ten of its revolutions. This extended series of 
observations furnished the data for a critical examination of the elements 
of the comet's orbit, and Prof Encke, having discussed them with 
elaborate care, reached the astonishing conclusion that the magnitude of 
the orbit was gradually diminishing, the periodic time growing shorter 
from revolution to revolution, and that the comet was certainly falling 
nearer and nearer to the sun ! 

To account for this extraordinary phenomenon, the learned astronomer, 
having exhausted all causes known to exist in the solar system, finally, 
with much hesitation, announced the theory of the comet's motion in a 
resisting medium. The existence of such a medium was in direct opposi- 
tion to all the received doctrines of astronomy, and the absolute necessity 
for its use in this instance was looked upon by astronomers with feelings 
of strong distrust. But Encke argued that such a medium might exist, 
of such*exceeding tenuity as not sensibly to affect the movements of the 
ponderous planets, while a filmy mass of vapor, such as this comet un- 
doubtedly was, might be very sensibly retarded in its original velocity, 
which would diminish continually the centrifugal force, and give to the 



t: ' 



132 ' STBUCTUBE OF THE UNIVERSE. 

central attraction of the sun a constantly increasing power, which would 
produce precisely the phenomena exhibited by the comet. 

With these views, Encke predicted the reappearance of the comet in 
1822. In consequence of its great southern declination at that period, it 
escaped all the European observers, and was only seen at Paramatta, by 
Rumker. The approach to the sun was in some degree confirmed by 
these observations, but it was impossible to reconcile all the observations 
with the hypothesis of a medium of given density. — The return in 1825 
was not favorable for deciding the question, which had now become one 
of the deepest interest. 

Its reappearance in 1828-9 was awaited with great anxiety by the 
friends and opponents of the new theory. The comet came round, and 
passed its perihelion approximately in accordance with the predictions, 
but the discrepancies from 1819 ud to 1829, with any theory, were so 
great, as to give much perplexity to those engaged in the computations. 
After long and patient examination, the cause of this difficulty was finally 
detected. The plane of the comet's orbit makes but a small angle with 
the orbit of Jupiter, and when the comet is in aphelion, or farthest from 
the sun, it always approaches very near to the path described by the 
planet. 

A time may then come when Jupiter shall be in the act of passing that 
part of its orbit very near to the aphelion point of the cometary ellipse, 
while the comet occupies its aphelion > bringing these bodies into close 
proximity, and producing excessive perturbations in the movements of 
this almost spiritual mass. Such, indeed, was the configuration between 
the returns of 1819 and 1829, on which occasion the comet was 
delayed in its return to its aphelion nearly nine days, by the powerful at- 
traction of Jupiter. Under these circumstances, any error in the assumed 
mass of the planet would exhibit itself in an exaggerated form in the per- 
turbations of the comet. But it was believed in the outset of this inves- 
tigation, that the mass of Jupiter, employed by Laplace in his theory of 
the planets, and computed by Bouvard could be relied on as accurate. 
Indeed, Laplace had applied the calculus of probabilities, and had found 
that there was but one chance out of eleven millions that the mass he had 
adopted could be in error by the one hundredth part of its value. 

Suspicion, however, having been aroused with reference to the mass of 
Jupiter, efforts were at once commenced to sift thoroughly the matter, and 
three different computers of high reputation undertook the determination 
of Jupiter's mass by different processes. Encke obtained a mass from 
the perturbations of the small planet Vesta, Nicolai from the perturbations 
of Juno, and Airy reexamined the original measures of the elongations of 
Jupiter's satellite, made new measures, and thus obtained new data for 
the resolution of the problem of Jupiter's mass. The results obtained by 
the three astronomers agreed in a most remarkable manner, and proved 



THE COMET ARY WORLD. 133 

incontestably that Laplace's value of the mass of this planet was in error 
more than four times the hundredth part of its value and that, instead of 
requiring 1,070 globes of the magnitude of Jupiter to balance the sun, 
only, 1,049 were necessary. 

With the new mass of Jupiter it seemed possible by admitting a resist- 
ing medium, to account for all the perturbations of Encke's comet, and 
for a time this theory seemed to receive greater consideration from dis- 
tinguished men. The appearance of Halley's comet in 1835 again threw 
great doubt over the subject, for it was found impossible to reconcile the 
movements of the two comets with any assumed density of a resisting 
medium". Some have been disposed to adopt the idea that the revolution 
of the planets, for ages, in the same direction, in this supposed ethereal 
fluid, has impressed upon it a Certain amount of motion in the same 
direction, and that those comets which chance to revolve with the current 
will be found to be operated upon differently from those which may 
happen to come into our system in a direction opposed to the current. 
. I confess, frankly, that my own mind has always revolted against the 
doctrine of a resisting fluid. — There are so many ways in which the single 
phenomenon of the gradual approach of Encke's comet to the sun may be 
accounted for, without resorting to an hypothesis which involves the en- 
tire destruction of the planetary system, whose perpetuity has been so ef- 
fectually provided for by the great Architect of the universe, that it would 
require the most unequivocal testimony to secure the full consent of my 
own mind to the adoption of this remarkable theory. It is proper, however, 
to say, that it has long been received with favor by men to whose judgment 
I am generally disposed to yield with implicit confidence. 

. Leaving the further consideration of this subject for the present, we 
proceed to the examination of another comet of short period, which has 
excited great attention, especially in its recent return. As. early as 1805, 
Prof. Gauss, in computing the elements of the orbits of the comets of that 
year, found one which seemed to complete its revolution in about, six 
years. This comet, however, was lost sight of, and it was not until. 1826 
that M. Biela discovered the same comet on its return to its perihelion. 
This discovery appears to have been the result of computation, but how 
far the investigation was carried, I have never been able to learn. 

The same object was also discovered by M. Gambart about the same 
time, who, on fixing its elements, found that it performed its revolution 
about the sun in an ellipse, with a period of six and three-quarter 
years. This comet, like Encke's, is only to be seen with the telescope. 
It presents no solid, or even well defined nucleus, and' appears to be a 
mere vapory mass, of exceeding tenuity. Taking into account the dis- 
turbing influence of Jupiter, the returns of Biela's comet, as predicted, 
agreed well with observation, and gave confidence in the theory on which 
the predictions were founded. 



134 STRUCTURE OF THE UNIVERSE. 

The return in 1832 excited the liveliest interest throughout the civil- 
ized world, in consequence of the fact that it was discovered from compu- 
tation, that on the night of the 29th of October, this comet would pass a 
little within the earth's orbit, and those unacquainted with the subject 
received the impression from this announcement, that the earth and comet 
would come into collision, producing the most terrific consequences. 
Such was the consternation excited, throughout the city of Paris espe- 
cially, that the Academy of Sciences found it necessary to give to the sub- 
ject their serious attention, and finally gave the matter in charge to M. 
Arago, who produced an elaborate report on the subject of comets gener- 
ally, which served to calm the popular apprehension, and has proved to 
be a valuable addition to our knowledge on this difficult subject. 

In this report, M. Arago, showed that the comet would indeed cross the 
earth's track at the time predicted, but at the moment of crossing, the 
earth would be some fifty-five millions of miles distant from the point 
occupied by the comet, and could not experience the slightest possible 
influence from such a body, at such a distance. 

If the comet had been delayed in its approach for thirty days, by any 
disturbing cause, then, indeed, the earth and comet would have filled at 
the same time the point where their orbits intersect, and the dreaded 
collision would have taken place. The consequences of such a shock it 
is impossible to conjecture, but reasoning from the known physical 
condition of the comet, none of the terrible disasters so generally antici- 
pated would have occurred. The exceeding rarity of the matter compos- 
ing this body may be inferred from the statements of Sir John Herschel. 
" It passed," says he, " over a small cluster of most minute stars of the 
16th and 17th magnitude ; and when on the cluster presented the appear- 
ance of a nebula resolvable, and partly resolved, the stars of the cluster 
being visible through the comet. A more striking proof could not have 
been offered of the extreme translucencv of the matter of which the comet 
consists. The most trifling fog would have effaced this group of stars, 
yet they continued visible through a thickness of cometic matter which, 
calculating on its distance and apparent diameter, must have exceeded 
50,000 miles, at least towards its central parts. That any star of the 
cluster was centrally covered, is indeed more than I can assert ; but the 
general bulk of the comet might be said to have passed centrally over the 
group T 

Such is the nature of the body from whose contact the ignorant appre- 
hended the most fearful convulsions. Olbers, who studied the subject 
with great care, was disposed to think that in case the earth had passed 
directly through the comet, no inconvenience would have occurred, and no 
change beyond a slight influence on the climate would have been expe- 
rienced. 

It is useless to speculate with reference to the probable consequences 



THE COMET ARY WORLD. 135 

of a collision, which there is scarcely one chance in millions can ever 
occur. Science has as yet discovered no guarantee for any planet against 
the possible shock of a comet ; but an examination of the delicate adjust- 
ments of our own system, and those of Jupiter and Saturn, would seem to 
indicate to us that in all past time no derangement has ever occurred from 
such' a cause. 

The last return of Biela's comet was marked by a phenomenon unex- 
ampled, so far as I know, in the history of these wandering bodies. 
True to the predictions of Santini, the comet first became visible 
on the evening of the 26th of November, 1845, and in the precise 
point which had been assigned by theory. De Vico, the director of the 
observatory at Rome, was the first to catch a glimpse of the expected 
comet. Nothing remarkable in its appearance was noticed, until about 
the 29th of December, when Mr. E. C. Herrick, of New Haven, pointed 
out to several friends what he regarded to be a sort of anomalous tail, but 
shooting out from the head of the comet in a direction entirely at variance 
with the usually received theory, that the tail is always opposite to the 
sun. In this supposed tail a kind of knot was noticed, brighter and more 
condensed than any other part. Owing to insufficient optical power, the 
true character of the phenomenon was not fairly detected by Mr. Herrick. 

On the night of the 12th of January, 1848, Lieut. Maury, in charge of 
the observatory at Washington City, discovered that what had hitherto 
appeared as a single body, was actually composed of two distinct and 
separate comets. This most extraordinary fact was immediately announced, 
and the double character was observed at all the principal observatories 
in Europe and the United States. There can be no doubt whatever as to 
the reality of the appearance. The comet actually became double, and 
the two parts, bound together by some inscrutable bond, continued their 
swift journey through space, pursuing almost exactly the route predicted 
for the single comet. 

From measures obtained by Prof. Challis, of Cambridge, England, on 
the 23d of January, 1846, the two comets were separated from each other 
by a distance equal to about one-thirteenth the apparent diameter of the 
sun. On the 28th of the same month, Sir John Herschel records the 
following notices : — " The comet was evidently double, consisting of two 
distinct nebulas, a larger and a smaller one, both round, or nearly so, — ■ 
the one in advance faint and small, and not? much brighter in the middle; 
the one which followed nearly three times as bright, and one and a half 
times larger in diameter, and a good deal brighter in the middle, with an 
approach to a stellar point. 

On the evening of the 9th of February, having returned to the observ- 
atory at Cincinnati, after an absence of more than two months, I had an 
opportunity of beholding, for the first time, these wonderful objects, with 
the twelve inch refractor. The moon was nearly full, and yet the comets 



136 STEUCTUBE OF THE UNIVERSE. 

were distinctly visible, both included within the limits of the field of 
view of the instrument, and separated from each other by a distance equal 
to about the eighth part of the sun's diameter. The preceding comet was 
evidently the brighter of the two. 

Clouds prevented a continuous examination of the comets from night 
to night, but on the evening of the 21st of February, I was surprised to 
rind a remarkable change in the relative brilliancy of the two parts. On 
that evening the following comet was very decidedly brighter than its 
companion, and from observations made elsewhere, the change of relative 
brightness seems to have been effected about the 13th or 14th of Febru- 
ary. The change was observed by Prof. Encke, of Berlin, as early as the 
14th. On the evening of the 21st of February, both comets exhibited 
distinct trains of light, extending from the sun, and in directions parallel 
to each other. The centre of the nucleus of each comet was brighter 
than the surrounding portions, but there was no stellar point visible. The 
nebulosity of the two points did not intermingle. 

The distance between the comets increased from day to day, until, on 
the 25th of February, they were separated by an amount equal to 445 
seconds of arc, or between a fourth and fifth part of the sun's diameter. 
A part of the increase of distance was only apparent, arising from the 
approach of the comets to the earth, but the comets were actually reced- 
ing from each other while pursuing their rapid flight through space. 

Neither did the line joining the central points of the comets remain 
parallel to itself. From the 23rd of January to the 11th of February, 
this line shifted its position by an amount of angular motion equal to 8° 
as is shown by a comparison of the measures of Challis and Encke. By 
the 21st of February, this angular motion had been nearly destined by 
a retrograde movement, and thus the comets were seen to oscillate about 
each other, according to some mysterious law which has never been re- 
vealed. Such is a brief sketch of the phenomena presented by Biela's 
comet in its late return. Its next appearance will be looked for with 
deep interest, to confirm or destroy certain theories which have been pro- 
pounded to explain its duplex character. 

While the periods of the comets which we have thus far considered are 
comparatively short, those of others which have visited our system have 
been ascertained to extend to many thousands of years. The great comet 
of 1811, one of the most brilliant of modern times, in consequence of its 
remaining visible for nearly ten months, gave ample opportunity for the 
investigation of the elements of its orbit. After a careful investigation, 
M. Argelander fixes its period of revolution at 2,888 years. B^essel had 
examined the same subject previously, and probably with less attention, 
but obtained a period even greater than Argelander's, amounting to 3,383 
years. 

The comet of 1807 also occupied the attention of Bessel. A long series 



THE COMET ABY WORLD. 137 

of observations furnished the data for computing its elements. The pa- 
riodic time was fixed at 1,543 years. These computations are necessarily 
only approximate. The difficulty of obtaining accurately the periodic 
time increases with the length of the period, and all that can be done is 
to fix a limit below which it cannot fall. These vast periods give to us 
the means of learning somewhat of the great distance to which these 
objects penetrate into space. The comet of 1811, having a period proba- 
bly three thousand times greater than that of our earth, must revolve at 
a mean distance from the sun of more than 80,000,000,000 of miles, and 
in consequence of its very near approach to the sun at its perihelion, its 
greatest distance cannot fall below 160,000,000,000 of miles ! 

Great as this distance is, it is perfectly certain that there are many 
comets whicli revolve in orbits far more extensive than the one described 
by the comet of 1811. Indeed, there seems to be no limit to the distance 
to which these bodies may sweep outward from the sun ; and their return 
depends simply on the fact whether they recede so far as to fall within 
the attractive influence of some other sun, towards which they begin to 
urge their flight, and through whose system of planets they carry the 
same apprehensions of danger which have been caused in our own. 

In reflecting on these singular objects we are led to inquire what they 
are, whence their origin, and by what laws are the vast trains of light 
which occasionally distinguish them developed ? Arago divides comets 
into three classes, with reference to their physical constitution. He thinks 
they occasionally appear round, and with . well defined planeta^ disks, 
showing them to be solid opaque bodies, in all.respects resembling planets, 
and only differing from these in the great eccentricity of their orbits. In 
confirmation of this opinion, he asserts that comets have been seen to 
transit the sun, and when passing between this luminary and the eye of 
the spectator, they appear round and black, like the planets Mercury and 
Venus, when seen under the same circumstances. An example of this 
kind occurred on the 18th of November, 1826, when the transit of a comet 
across the sun was witnessed by two persons, widely separated from each 
other. 

A second class of comets comprehends those in which there is a nucleus, 
but devoid of opacity, permitting the light to penetrate through even 
that portion which may possibly be solid. The third class^ and that by 
far the most numerous, comprehends those comets destitute, entirely, of 
any solid nucleus, consisting of matter so attenuated as to compare fairly 
with nothing of which we have any knowledge on the earth's surface. The 
comets named for Encke and Biela appear to belong to this class ; and 
even Halley's comet, according to the opinion of Sir John Herschel, 
seems, at its last return, to have been entirely turned into vapor in its 
perihelion passage. 

No theory, with the exception Laplace's nebular hypothesis, has ever 



138 STRUCTURE OF THE UNIVERSE. 

been framed to explain the origin of these wandering bodies. This is not 
the place to enter into a full development of this subject. — A few hints 
only can be given. Laplace, following up the speculation of Sir William 
Herschel, applied the theory of that astronomer to the formation of the 
solar system, comprehending the comets, as well as the planets and their 
satellites. This theory supposes that the original chaotic condition of the 
matter of all suns and worlds was nebulous, like the matter composing 
the tails of comets. Under the laws of gravitation, this nebulous fluid, 
scattered throughout all space, commences to condense towards certain 
centres. The particles moving towards these central points, not meeting 
with equal velocities, and in opposite directions, a motion of rotation is 
generated in the entire fluid mass, which in figure, approximates the 
spherical form. 

The spherical figure once formed, and rotation commenced, it is not 
difficult to conceive how a system of planets might be produced from this 
rotating mass, corresponding, in nearly all respects, to the characteristics 
which distinguish the planets belonging to our own system. If, by radia- 
tion of heat, this nebulous mass should gradually contract in size, then a 
well known law of rotating bodies would insure an increased velocity 
of rotation. This might continue until the centrifugal force, which increases 
rapidly with the velocity of the revolving body, would finally come to 
be superior to the force of gravity at the equator, and from this region 
a belt of nebulous fluid would thus be detached in the form of a ring, 
which would be left in space by the shrinking away of the central globe. 
The ring thus left would generally coalesce into a globular form, and 
thus would present a planet with an orbit nearly, if not quite circular, 
lying in a plane nearly coincident with the plane of the equator of the 
central body, and revolving in its orbit in the same direction in which 
the central globe rotates on its axis. 

As the globe gradually contracts, its velocity of rotation continually 
increasing, another ring of matter may be thrown off, and another planet 
formed, and so on, until the cohesion of the particles of the central mass 
may finally be able to resist any further change, and the "process ceases. 

The planetary masses, while in the act of cooling and condensing, may 
produce satellites in the same manner, and by the operation of the same 
laws by which they were themselves formed. Strange and fanciful as 
this speculation may appear, there are many facts which tend strongly to 
give it more than probability. It accounts for all the great features of the 
solar system, which, in its organization, presents the most indubitable evi- 
dence that it has resulted from the operation of some great law. 

The sun rotates on an axis in the same direction in which the planets 
revolve in their orbits ; the planets all rotate on their axes in the same 
direction ; they all circulate around the sun in orbits nearly circular, in 
the same direction, and in planes nearly coincident with the plane of the 



THE COMETART WORLD. 139 

sun's equator. The satellites of all the planets, with one single exception 
revolve in orbits nearly circular, but little inclined to the equators of their 
primaries, and in the same direction as the planets. So far as their rota- 
tion on axes has been ascertained, they follow the general law. — In one 
instance alone we find the rings of matter have solidified in cooling, with- 
out breaking up or becoming globular bodies. This is found in the rings 
of Saturn, which present the very characteristics which would flow from 
their formation according to the preceding theory. They are flat and 
thin, and revolve on an axis nearly, if not exactly, coincident with the 
axis of their planet. Their stability, as we have seen, is guaranteed by 
conditions of wonderful complexity and delicacy, and the adjustment of 
the rings to the planet, (humanly speaking), would seem to be impossible 
after the formation of the planet. — At least it is beyond our power to con- 
ceive how this could be accomplished by any law of which we have any 
knowledge, and we must refer their structure at once to the fiat of Omnipo- 
tence. 

Granting the formation of a single sun by the nebular theory, and we ac- 
count at once for the formation of all other suns and systems through- 
out all space ; and according to the advocates of this theory, the comets 
have their origin in masses of nebulous matter occupying positions inter- 
mediate between two or more great centres, and held nearly in equilibrio, 
until, finally, the attraction of some one centre predominates, and this 
uncondensed filmy mass commences slowly to descend towards its con- 
trolling orb. This theory would seem to be sustained, so far as a single 
truth can sustain any theory, by the fact that the comets come into our 
system from all possible directions, and pursue their courses around the 
sun either in accordance with, or opposed to, the direction in which the 
planets circulate. Their uncondensed or nebulous condition results from 
the feeble central attraction which must necessarily exist in bodies com- 
posed of such small quantities of matter. Moreover, in some cases at 
least, there is reason to believe, that in their perihelion passage they are 
entirely dissipated into vapor by the power of the sun's heat, and may 
thus revolve for ages, going through alternate changes of solidification and 
evaporation. 

But whence come the enormous trains of light which sometimes attend 
these wandering bodies ? — The last return of Halley's comet has furnished 
the data for the positive illustration of this mysterious subject. Sir John 
Herschel, after a careful and most elaborate examination of all the physi- 
cal characteristics of this comet, comes to the conclusion that the figure of 
the comet, envelope and tail, could not be a figure of equilibrium under 
the law of gratification. He is therefore compelled to bring in a repulsive 
force to explain the phenomena. 

I cannot do better than to quote his own language in this bold intro- 
duction of a new power. — " Nor let any one be startled at the assumption 



140 STRUCTURE OF THE UNIVERSE. 

of such a repulsive force as here supposed. Let it be borne in mind that 
we are dealing (in the tails of comets) with phenomena utterly incompat- 
ible with our ordinary notions of gravitating matter. If they be material 
in that ordinary received sense which assigns to them only inertia and 
attractive gravitation, where, I would ask, is the force which can carry them 
round in the perihelion passage of the nucleus, in a direction pointing 
continually from the sun, in the manner of a rigid rod, swept round by 
some strong directive power, and in contravention to all the laws of planetary 
motion, which would require a slower angular motion of the more remote 
particles, such as no attraction to the nucleus could give them, be it ever 
so intense ? The tail of the comet of 1680, in five days after its peri- 
helion passage, extended far beyond the earth's orbit, having, in that 
brief interval, shifted its angular position nearly 150°. Where can we 
find, in its gravitation either to the sun, or to the nucleus, any cause for 
this extravagant sweep ? 

" But again, where are we to. look (if only gravity be admitted) for any, 
reasonable account of its projection outward from the sun, putting its 
angular motion out of the question ? Newton calculated that the matter 
composing its upper extremity quitted the nucleus only two days previ- 
ous to its arriving at this enormous distance." 

Herschel argues the inadequacy of gravitation to account for. these 
wonderful phenomena. The velocity with which the matter composing 
the tail shot forth from the head of the comet, from the sun, was far 
greater than that which the sun could impress on a body falling to it, 
even from an infinite distance. — An energy of a different kind from gravi- 
tation, and far more powerful, must exist, to produce ■ such results. If, 
then, we are forced to the admission that a power exists in the sun cap- 
able of repelling matter of a certain quality existing in comets, a way is 
opened for the explanation of some of the most difficult problems with 
which the mind. has. been obliged to contend. 

The diminution of the periodic time of Encke's comet has. led some 
astronomers to adopt the idea of the existence of a resisting medium. 
But in case the sun possesses the power of repelling the matter of comets 
in their perihelion passage, a part of the matter thus repelled may be 
driven entirely beyond the attractive influence of the nucleus, and be 
irrecoverably lost. In this case, a diminution of mass would inevitably 
involve a like diminution of periodic time, a contraction of the orbit, and 
all the phenomena presented by this mysterious object. Herschel even 
thinks it possible, on this theory, to account for the separation of Biela's 
comet into two distinct objects, and it appears to me that it presents the 
most reasonable explanation of the luminous appearance seen at certain 
seasons of the year, called the zodiacal light.- — This phenomenon appears 
to be a ring of nebulous matter surrounding the sun, and some of whose 
particles are sustained at a much greater distance than could be accounted 



- 



THE COMET ART WOULD. 141 

for by gravitation. Admitting the repulsive power already adverted to, 
there is no difficulty in understanding how this nebulous ring may be 
sustained at a vast distance from the sun. 

Here we freely admit that we enter the confines of the unknown. 
We have left the solid ground of truth and certainty and are pushing our 
investigations into the dim twilight of the invisible and uncertain. But 
as antiquity predicted that the time would come when the comets would 
be traced in their career, their periods revealed, and their orbits ascer- 
tained, sso we may confidently hope that, at no very distant day, all the 
mysteries which hang around these chaotic worlds will be fully revealed, 
and a knowledge of their physical condition shall reward the long study 
and deep research of the human mind. 



LECTURE IX. 

THE SCALE ON WHICH THE UNIVEKSE IS BUILT. 

Thus far our attention has been directed to an examination of the 
achievements of the human mind within the limits of our own peculiar 
system. We have swept outward from the sun through the planetary 
worlds, until we have reached the frontier limits of this mighty family. 
Standing upon the latest found of all the planets, at a distance of more than 
3,000,000,000 of miles from the sun, we are able to look backwards, and 
examine the worlds and systems which are all embraced within the vast cir- 
cumference of Neptune's orbit. An occasional comet, overleaping this 
mighty boundary, and flying swiftly past us, buries itself in the great abyss 
of space, to return after its " long journey of a thousand years," and re- 
port to the inhabitants of earth the influences which have swayed its move- 
ments in the invisible regions whither it speeds its flight. 

The magnificence and complexity of the great system of planets and 
satellites and comets which constitute the sun's retinue ; the immense mag- 
nitude of some of these globes ; their periods of revolution, and reciprocal 
action, would seem to furnish a sufficient exercise, not only for the highest 
intellectual efforts, but for the entire energy which the human mind can 
exert. But the whole of this stupendous scheme, as we shall soon see, is 
but an infinitesimal portion of the universe of God, one unit among the 
unnumbered millions which fill the crowded regions of space. — Standing at 
the verge of the planetary system, we find ourselves surrounded by a mul- 
titude of shining orbs, some radiant with splendor, others faintly gleaming 
with beauty. The smallest telescopic aid suffices to increase their number 
in an incredible degree, while with the full power of the grand instruments 
now in use, the scenes presented in the starry heavens become actually 
so magnificent as to stun the imagination and overwhelm the reason. 
Worlds and systems, and schemes and clusters, and universes, rise in sub- 
lime perspective, fading away in the unfathomable regions of space, until 
even thought itself fails in its efforts to plunge across the gulf by which 
we are separated from these wonderful objects. 

In our measurements within the limits of the solar system, the radius of 
the earth's orbit has sufficed for a unit with which to exhibit the distances 
of the planets and comets. Great as is this unit, measuring no less than 
95,000,000 of miles we shall soon find it far too minute and insignificant 
to serve in our researches with reference to the grand scale of the visible 



144 STRUCTURE OF THE UNIVERSE. 

universe. To obtain comprehensible ideas with reference to the inter- 
stellar spaces, we shall be obliged to call to our aid a unit, not exactly of 
distance, but of velocity ; and before entering on the full exhibition of the 
main object of this lecture, permit me to direct your attention to a re- 
markable discovery, by which the important fact has been revealed, that 
light does not pass instantly from a luminous body to any remote object on 
which it may fall, but with a progressive motion, whose actual velocity has 
been ascertained. The important bearing of this discovery will become 
apparent as we advance in our examination of the sidereal heavens. 

After the motions of the four moons of Jupiter had been sufficiently 
observed to construct tables of their movements, with a view to predict 
their eclipses, some unaccountable phenomena presented themselves, which, 
for a long time, baffled all efforts to explain them. It should be remembered, 
that the orbit of Jupiter encloses that of the earth, and when the two plan- 
ets happen to be on the same side of the sun, and in a straight line passing 
through that orb, they are then at their least distance from each other, and 
are said to be in conjunction. Now suppose Jupiter to remain stationery, 
at the end of half a year the earth will have reached the opposite point of 
her orbit, and will now bemore distant from Jupiter by an amount equal to 
the diameter of her orbit, or nearly 200,000,000 of miles. Retaining care- 
fully these positions in the mind, we shall follow the facts about to be pre- 
sented with the greatest ease. 

It was found that those eclipses of Jupiter's satellites, which occurred 
while the earth and planet were at their least distance from each other, 
always came on sooner than the time predicted by the tables ; w r hile, on the 
contrary, those which took place when the planets were most remote from 
each other, occurred later than the computed time. A still more extended 
examination of these remarkable phenomena demonstrated the fact, that 
the discrepancies depended evidently on the absolute increase and decrease 
of distance which marked the relative position of the planets in their rev- 
olutions around the sun. For a long time, no explanation of these un- 
deniable truths could be found, until the mystery was finally solved by 
Roemer, a Danish astronomer, who, with admirable sagacity, traced these 
irregularities to their true source, and found that they arose from the fact 
that light traveled through space with a finite and measurable velocit}\ 

The explanation is simple. When Jupiter and the earth are at their 
least distance from each other, the stream of light flowing from the satel- 
lite of the great planet traverses a shorter space to reach the eye of the 
observer on the earth, by nearly 200,000,000 of miles, than when the plan- 
ets are most remote from each other. In case, therefore, this stream is in 
any way cut off, it will run out sooner in the first than in the second posi- 
tion, by the time required to pass over the diameter of the earth's orbit. 
The stream of light is actually shorter, by 200,000,000 of miles, in the first 
than in the second position of the planets. 



THE SCALE ON WHICH THE UNIVERSE IS BUILT. 145 

Now the satellites of Jupiter receive their light from the sun ; — they re- 
flect this light to the earth, and when the body of their primary is inter- 
posed between them and their source of light, they are eclipsed ; their light 
is cut off ; its flow is interrupted ; and when the stream of light starting 
from them at the instant the supply is cut off shall have run out, then, ana 
not till then, does the satellite become invisible. This explanation ac- 
counted for all the phenomena in the most beautiful manner. 

The tables had been constructed from the mean of a great number of 
observed eclipses. Hence, those which took place while Jupiter and the 
earth were near to each other, would happen earlier than prediction ; while 
those taking place when the planets were at their greatest distance, would 
occur later than the time given by the tables. But the velocity with which 
this mysterious, subtle, intangible substance called light, flew through the 
regions of space, as determined by this wonderful theory, was so great as 
to startle the minds of even its strongest advocates, and to demand the 
most positive testimouy to induce the belief of those disposed to scepticism. 
It was found to traverse a distance equal to the entire diameter of the 
earth's orbit, or 190,000,000 of miles, in about 16 minutes ! — giving a veloc- 
ity of 12,000,000 of miles per minute, or 192,000 miles in each second of 
time! 

It is not our purpose to enter into any investigation as to the true 
theory of light, whether it be an actual emanation from a luminous body 
of material particles, or whether it be a mere vibratory or undulating mo- 
tion produced by luminous bodies on some ethereal medium. My only 
object, at this time, is to assert the undoubted fact, that in case a lumi- 
nous body were to be suddenly called into being, and located in space at 
the distance of 12,000,000 of miles from the eye of an observer, who was 
on the look-out for its light, this light would not reach him until one 
minute after the creation of the object ; and should it suddenly be struck 
from existence, the same^ observer would behold it for one minute after 
the extinction. 

Should any mind revolt from these statements — should the difficulty 
of the investigation, and the incredible velocity of light, demand higher 
and better evidence, before full faith can be given to the theory, I can 
only say that this evidence shall be given before we close this discussion, 
and with a fullness and clearness which shall set all doubts at defiance. 

I now proceed to an examination of the great problem of the parallax 
of the fixed stars, a problem which has taxed the ingenuity of the 
greatest mind, and which has called into requisition the most admir- 
able skill for a period of more than 300 years. A familiar explana- 
tion of the nature of this problem may prepare the way for a rapid 
sketch of the various means which have been employed in its solu- 
tion. If it were possible to measure on the earth's surface a base line 
of a thousand miles in length, by locating an observer at each extremity 

10 



U6 



STRUCTURE OF THE UNIVERSE- 



of this base' with instruments suitable to fix the moon's place among the 
fixed stars, the telescopes of those two observers, directed to the moon's 
centre at the same instant would incline towards each other, and the 
visual ray from each of those instruments would meet at the moon's 
centre, and form an angle with each other. This angle, or opening of 
the visual rays, is called the parallax, and in case the object under ex- 
amination were a fixed star, then would the angle in question be called 
the parallax of the fixed star. 

It is readily seen that when the length of the base is known, and the 
parallactic angle measured, then the length of the visual ray may be at 
once determined, and the distance of the object is made known by the 
simplest rules of geometry. Parallax, then, in general, is the apparent 
change in the place of an object occasioned by the real change in the 
place of the spectator. 

The whirling of the trees of a forest, produced by the rapid speed of 
the beholder along a railway, is a parallactic motion, and becomes less 
and less perceptible as the velocity of the spectator diminishes, or as the 
distance of the seemingly moving object becomes greater. To measure the 
distance of the fixed stars is then equivalent to determining the amount 
of parallactic change in their relative positions occasioned by the actual 
change of the positions from which they may be viewed by a spectator 
on the earth's surface. 

With the sun and moon and planets, a base line equal to the earth's 
diameter, or about 8,000 miles has sufficed to produce a sensible and meas- 
urable parallax ; but when we extend our visual rays to a fixed star, from 
the extremities of this base, their directions, to our senses, are absolutely 
parallel, or, in other language, the parallax arising from such a base is 
perfectly insensible. This first effort indicates, at once, the vast distance 
of the objects under examination ; for such is the accuracy with which mi- 
nute spaces are now divided, that parallax may be detected in case the 
object is even 160,000 times farther distant than the length of the base 
line. 

When the orbitual motion of the earth was first propounded by Coper- 
nicus, and it was asserted to revolve in an ellipse of nearly 600,000,000 of 
miles in circumference, and with a motion so swift that it passed over no 
less than 68,000 miles in every hour of time, the opponents of these start- 
ling doctrines exclaimed No ! this is impossible ; for if we are sweeping 
around the sun in this vast orbit, and with this amazing velocity, then 
ought the fixed stars to whirl round each other, as do the forest trees to 
the traveler flying swiftly by them. 

But the stars of heaven do not move. Seen from any point, and at any 
time, their places are ever the same, — fixed, immutable, eternal, — the 
bright and living witnesses of the extravagance and absurdity of this new 
and impossible theory. To this reasoning, which was well founded, and 



THE SCALE UPON WHICH THE UNIVERSE IS BUILT, 147 

without sophistry, the Copernicans could only reply, that such was the 
euormous distance of the fixed stars, that no perceptible change was occa- 
sioned by the revolution of the earth in its orbit. But this was mere asser- 
tion and the opponents met the statement by this very plain exhibition 
of the case. — You who believe in the doctrines of Copernicus assert that 
the earth revolves on an axis, which, as it sweeps round the sun, remains ever 
parallel to itself. This axis prolonged meets the celestial sphere in a 
point called the north pole. Now as the earth describes an orbit of near- 
ly 200,000,000 of miles in diameter, its axis prolonged will cut out of the 
sphere of the heavens a curve of equal dimensions, and the pole will ap- 
pear to revolve and successively fill every point of this celestial curve in 
the course of the year. Now the north pole does not revolve in any such 
curve ; it is ever fixed, and your theory is false. The Copernican could 
only reply, that all the premises were true, but that the conclusion was, 
false. The pole of the heavens did revolve in just such a curve as stated 
but such was the distance of the sphere of the fixed stars, that this curve 
of 200,000,000 of miles in diameter was reduced to an invisible point! 

Three hundred years have rolled away since this controversy began. 
The struggle has been long and arduous. The mind, baffled in one direc- 
tion, has directed its energies in another — failing in one mode of research, 
it devises another, and thus struggling onward for three long centuries, it 
at length triumphs. The facts are developed and the truth of the grand 
theory of Copernicus is vindicated and established, and the accuracy of 
these incredible statements is proved in the clearest manner. 

As this discussion exhibits, clearly and beautifully, the progressive advan- 
ces of human genius, I shall be pardoned for entering, at some length, into 
an examination of the various attempts which have been made to resolve 
the problem of the parallax of the fixed stars. Indeed, the distance of the 
nearest fixed star is to become the unit of measure with which we are to 
traverse the innumerable worlds and systems by which we are surround- 
ed, and on the accuracy with which it shall be determined will depend 
the correctness of the survey which we are soon to make. 

Failing entirely in obtaining any parallactic angle with a base line of 
8,000 miles in length, the earth was employed to transport the observer 
from the first point of observation to a distance of 190,000,000 of miles, 
there again to erect his telescope, and to send up his second visual ray to 
the far distant star, in the hope of finding a parallactic angle with a base 
of such enormous extent. 

Permit me to illustrate the nature of this investigation, Suppose from 
the centre of a plane a solid granite rock, deep sunk and immovable, 
rears its head far above the mists and impurities which float in the lower 
air. Ascending to the summit, the astronomer hews out some rough peak 
into the form of a vertical shaft. To this solid shaft he bolts the metallic 
plates which shall bear his telescope. The instrument is of a size and 



148 STRUCTURE OF THE UNIVERSE. 

power commensurate with the grand objects which it is required to ac- 
complish. Placed in a position such that its axis shall be exactly vertical 
it is screw-bolted and iron-bound to the solid rock with fastenings which 
shall hold it from year to year, fixed and immovable as its rocky base. 

To give more perfect precision to his work, the astronomer places 
in the focus of his eye-piece two delicate lines made from the spider's 
web, of a minuteness almost mathematical, which by crossing at right 
angles, form a point of the utmost precision exactly in the axis of the tele- 
scope. These are in like manner fixed immovably in their places, and now 
the machinery is prepared with which the observations are to be con- 
ducted. 

Suppose the observations to commence to-night. — On placing the eye 
to the telescope, and looking directly up to the zenith, a star enters the field 
of the instrument, and borne along by the diurnal notion of the heavens, 
advances towards the central point determined by the intersection of the 
spider's lines. In passing across the field of view, its minute diameter is 
exactly bisected by one of these delicate lines, and the exact moment, to 
the hundredth part of a second of time, is noted at whieh it passes the 
central point. This observation completed with all posssble precision, in 
case no change in the apparent place of the star is produced by the revo- 
lution of the earth in its orbit, or by any other cause, on each successive 
night throughout the entire year the same phenomena will be repeated in 
the same precise order. When the hour comes round, the star will enter 
the field, thread the spider's line, and reach the central point at the same 
precise instant, night after night even for a thousand revolutions of the 
earth on its axis. 

Such, then, is the delicate means employed in the examination of the 
problem of the parallax of the fixed stars ; and nearly in this way did 
Bradley, the great English astronomer, prosecute this intricate investiga- 
tion. If any change in the star's place is occasioned by the revolution of 
the earth in its orbit, sweeping, as it does, the spectator round the circum- 
ference of a track nearly 200,000,000 of miles in diameter, it is easy to 
compute, not the amount, but the direction in which these changes will be 
accomplished. These computations were made by the astronomer, and all 
things being prepared, he commenced the series of observations which 
were to lead to the most important results. The discovery of absolute 
fixity in the star would be a great negative result, and any changes, no 
matter of what kind or character, could not fail to be detected. 

Night after night was the astronomor found at his post, and as the 
months rolled slowly away, he began to perceive that his star, which, for 
a long time threaded the spider's line as it was in the act of passing the 
field of the telescope, began slowly to work off from this line, at last abso- 
lutely separating itself from it, and failing to reach the central point of 
the f eld at the precise instant- first recorded. It soon became manifest 



THE SCALE UPON WHICH THE UNIVEBSE IS BUILT. 14$ 

that some cause or causes were operating to produce an apparent chang* 
in the place of the star, but what was the astonishment of Bradley to find 
that the changes in question could not be produced by parallax, for the 
motions detected were almost precisely opposite to those which would 
arise from this cause. 

Long years of laborious examination were finaly rewarded with two of 
the most brilliant discoveries ever accomplished by human skill and 
genius. The first of these demonstrated the fact that the sun and moon 
were so operating on the protuberant matter at the earth's equator as to 
cause the axis of the earth to oscillate or revolve in a minute orbit, nod- 
ding to and fro under the influence of the configurations of these two 
controlling bodies, and following, in the most absolute manner, their rela- 
tive positions. The effect of this variation, called nutation, is to cause 
all the stars to appear alternately to approach and recede from the pole. 
— The real effect is to move the pole by the same amount. 

The value of this change has been determined with the utmost precision, 
and although its entire effect does not shift the pole over a greater space 
than the fourth part of the apparent diameter of the planet Jupiter, its 
values, as deduced by different astronomers and by different processes, 
scarcely differ by the fraction of a second of space. As a specimen of the 
accuracy attained in these delicate measurements, I will give three values 
recently obtained by the Russian astronomers. — M. Busch, from Bradley's 
observations, obtains the value 9". 2320; M. Liendhal, from observations 
at Derpat, finds the value 9", 1361; M. Peters, from right ascensions of 
Polaris, observed at Derpat fixes the value at 9". 2164. — The mean of the 
three values is 9". 2231, the highest difference from which is less than the 
tenth part of one second of arc. 

Valuable as was this discovery, it was actually surpassed by the im- 
portance of the second, for which we are in like manner indebted to 
Bradley. This second phenomenon consisted in an apparent movement 
of all the fixed stars in a minute orbit, which was accomplished in a year 
for every individual, and showed, in the most absolute manner, that it 
depended in some way on the orbitual revolution of the earth. — For a 
long time, the true explanation of this phenomenon, which Bradley saw ' 
at once was not parallactic, eluded his highest sagacity. Potent thought 
and persevering reflection were, however, at last triumphant, and an ex- 
planation was finally reached, not only of the most satisfactory kind, but 
involving nothing less than an absolute demonstration of the orbitual mo- 
tion of the earth, and a full confirmation of the velocity of light, whose 
prodigious swiftness had staggered the faith of many anxious to credit so 
marvelous a statement. 

A few words will suffice to explain these phenomena. If we admit the 
progressive motion of light and the revolution of the earth in its orbit, it 
k manifest that the celestial bodies will not occupy in the heavens th* 



350 STRUCTURE OF THE UNIVERSE. 

places they appear to fill. Take, for example, the planet Jupiter, and 
even suppose the planet to be fixed. The telescope is directed to this 
object, and the light from the planet, streaming through the axis of the 
instrument, reaches the eye of the observer, and produces the visible image 
of the planet. But these very particles of light have occupied nearly 40 
minutes in passing from the planet to the eye of the observer. During 
these 40 minutes, the earth has progressed in its orbit some 37,000 
miles, and the spectator on the earth, borne along with it, must see the 
planet, not where it actually is but where it was in appearance some forty 
minutes before. The same effect, in kind, is produced on the places of 
the fixed stars, and is called aberration. Understanding, now, that sortie 
effect must arise from these causes, (the velocit}^ of light and the motion 
of the earth), let us endeavor to render its nature clear, and the results 
palpable. To accomplish this, we must resort to the simplest means of 
elucidation. 

Suppose a person were on the deck of a boat floating down the current 
of a river at any given rate per hour. As he moves steadily down the 
stream, he catches sight of an object on the shore, through which he pro- 
poses to send a rifle ball. The marksman will not aim directly at the ob- 
ject. Why? Because he knows that the rifle ball will partake of the 
boat's motion, and will be carried down, after it leaves the gun and be- 
fore it reaches the mark, a distance equal to the progressive motion of the 
boat during the time of flight of the ball. To strike the mark, he must 
therefore make this necessary allowance, and aim above it the required 
quantity. It is readily seen that the faster the boat moves, the greater 
will this allowance be. 

Now reverse the proposition, and suppose a rifle fixed on shore, and so 
directed as to fire a ball down the barrel of a gun on a moving boat. In 
case the two rifles are on the same exact level, and the axes of the barrels 
come precisely to coincide, it might be supposed that if the fixed one 
is fired at the exact instant the muzzles come precisely opposite to each 
other, that the ball from the one will pass down the other. But this 
from a moment's reflection, is found to be false. The fixed rifle must 
be fired before the moving one comes opposite, and the allowance must be 
made by knowing how long the ball requires to move from the one gun 
to the other, and with what velocity the moving piece is descending. 
This computation being accurately made, the ball from the shore might 
be made to enter the muzzle of the moving rifle ; but while it is progres- 
sing down the barrel, the barrel itself is progressing down the stream, and 
hence, to avoid the pressure of the ball against the upper side of the 
barrel, we must fix it in an inclined position, and the bottom of the barrel 
must be as far up stream as it will descend by the boat's motion during 
the progress of the ball down the barrel. Hence we see that the direction 
in which the barrel of the rifle which is to receive the ball is to be placed, 



TLTE SCALE UPON WHICH THE UNIVERSE IS BUILT. 151 

is determined by the velocity of the ball, and the velocity of the boat 
which bear the rifle. 

Now for the application. The particles of light coming from the fixed 
stars are the balls from the fixed rifle. The boat corresponds to the earth 
sweeping around in its orbit, and bearing with it the tube of the 
astronomer, down whose axis the particles of light must pass to reach the 
observer's eye. The velocity of the earth's motion is well known, and the 
amount by which the telescope must be inclined, to cause the light to 
enter, has been accurately determined, and from these two data the 
velocity of the light itself becomes known, and confirms, in the most 
satisfactory manner, the previously determined value of this incredible 
velocity, while the reality of the earth's motion is absolutely necessary to 
render the phenomena at all explicable. 

Such were the beautiful results reached by Bradley, and although noth- 
ing was gained with reference to the parallax, these preliminary discoveries 
were in themselves of the highest value, and prepared the way for sub- 
sequent observers, who, with better means and more delicate instrumental 
aid, might prosecute the same great investigation. 

Amid the numerous and diversified researches of Sir William Herschel, 
the problem of the parallax of the fixed stars could not fail to engage his 
attention by its difficulty and importance. He devised a new means of 
prosecuting this research, which seemed to promise the most certain 
success. In his exploration of the heavens with his powerful telescopes, 
he discovered the curious fact that many fixed stars which, to the unas- 
sisted eye, appear as single objects, under the space-annihilating power of 
the telescope, are seen to consist of two, sometimes of three or more, 
individual stars, so close to each other that, to the naked eye, they blend 
into a single object. 

Herschel, in the outset, conceived that this proximity of the stars was 
an accidental circumstance, and that where a pair could be found, in 
which one individual was about double the other in magnitude, it might 
reasonably be inferred that the smaller of the two was twice as deeply sunk 
in space as the larger. If this hypothesis could be shown to be true, then 
would these objects present an admirable means of detecting, with the 
greatest accuracy, any change in their relative positions, occasioned by 
the orbitual motion of the earth. In case their proximity was optical, or 
merely occasioned by the fact that the visual ray drawn to the one passed 
nearly through the other, it is manifest that, shifting greatly the position 
of the observer, the stars might be made to open out or close up on each 
other, or even revolve the one about the other. In employing this mode 
of investigation, the objects of comparison fell within the field of view of 
the same telescope, and almost all extraneous sources of error were 
eliminated. 

Such was the plan devised, or rather perfected by Herschel, (for his 



152 STRUCTURE OF THE UNIVERSE. 

predecessors had already suggested it), and on the prosecution of which 
he entered with the zeal which ever distinguished this great astronomer. 
When he commenced his researches, some half dozen double stars had 
been discovered and recorded. His first duty was to increase this number 
as rapidly as possible, and from his entire catalogue to select those best 
adapted to his purpose. Under his penetrating glance, the number of 
these curious duplex objects increased with astonishing rapidity, and he 
was himself startled with their frequent occurrence. However, with a 
mind fixed on his original design, he selected a large number of pairs, of 
such relative magnitudes, and in such positions, as promised the most 
certain success. Let it be remembered that many of these delicate objects 
were not divided from each other by a space greater than the thousandth 
part of the sun's diameter. 

To ascertain the apparent changes in the relative positions and distances 
erf the stars composing these pairs, Herschel measured, with every care, 
the distance which separated them, and took the direction of the line 
drawn from the centre of the one to the centre of the other. Variations 
of distance and position, occasioned by parallax, were easily computed in 
kind and character, and the great astronomer commenced and prosecuted 
his observations with sanguine hopes of success. One thing was certain : 
— all parallactic movements w T ould have a period of one year, since they 
arise from the annual revolution of the earth in its orbit, and at the end 
of this period the stars composing the double sets ought to return to the 
position occupied at the outset. What was Herschel's astonishment to 
find that, in many instances the stars composing these pairs were actually 
in motion ; but the movement was certainly not of a parallactic kind, for 
it neither agreed in direction or in period with the effects of parallax. 
Here was another grand discovery ! These double stars, which were scat- 
tered throughout the heavens with far greater profusion than accidental 
optical proximity could warrant, w r ere found to be magnificent systems of 
revolving suns ! They were united by the law of gravitation, and exhib- 
ited the wonderful spectacle of stupendous globes, moving in obedience 
to the same influences which hold the planets in their orbits, and guide 
the comets in their eccentric career. — This is not the place to enter into 
detail concerning these wonderful objects. 

While a new field of investigation, boundless and magnificent, was 
opened up to the human mind ; while the great discoverer of these far- 
sweeping suns was more than rewarded for his toil and labor, the original 
abject of his research was not only left unattained, but the method select- 
ed with so much reasonable hope of success, became utterly inapplicable. 
The parallactic and absolute motions of the systems of stars became so 
inextricably involved, that the imperfect micrometrical means of Herschel 
sould not separate them. 

Thus far, the efforts to obtain the distance of the stars had been un 7 



THE SCALE UPON WHICH THE UNIVERSE IS BUILT. 158 

availing. — A negative solution had indeed been reached. That their dis- 
tance was enormous, was made evident, from the fact that the parallax 
had remained insensible, even under the most careful and delicate in- 
strumental tests. Any absolute solution began almost to be despaired of, 
when hope was again revived by the magnificent refracting telescopes, 
for which the world was indebted to the skill and genius of the celebrated 
Frauenhofer, of Munich. — This great artist, aided by the profound science 
of Bessel, contrived and executed an instrument of extraordinary power, 
and especially adapted to the research for the parallax of the fixed stars. 

Armed with a micrometrical apparatus of wonderful perfection, and 
capable of executing measures of great, as well as minute distances, the 
telescope was so arranged as to be carried forward by delicate machinery, 
with a velocity exactly equal to the diurnal motion of the object under 
examination. — To give some idea of the delicacy of the contrivances with 
which these great telescopes have been provided, it is only necessary to 
state that the micrometer of the great Refractor of the Cincinnati obser- 
vatory is capable of dividing an inch into 80,000 equal parts ! — When 
mechanical ingenuity failed to construct lines of mathematical minute- 
ness, the spider lent his aid, and it is with his delicate web that these 
measures are accomplished. Two parallel spider's webs are adjusted in 
the focus of the eye-piece of the micrometer, and when the light of a small 
lamp is thrown upon them, the eye, on looking through the telescope 
sees two minute golden wires, straight and beautiful, drawn across the 
centre of the field of view, and pictured on the heavens. These are with- 
in the control of the observer. He can increase or decrease their dis- 
tance at pleasure, and so revolve them as to bring them into any position, 
every motion being accurately measured by properly divided scales. 

Suppose, then, it is desired to take the distance and position of the 
stars forming a pair. The telescope is directed to them, and they are 
brought to the centre of the field of view. The clock-work is set in ac- 
tion ; it takes up the ponderous instrument, weighing more than 2,500 
pounds, and with the most astonishing accuracy it bears it onward, keep- 
ing its mighty eye fixed on the object under examination. The observer 
is thus left with both hands free to make his measures. — He first revolves 
his micrometer spieler's lines round until one of them shall exactly pass 
from centre to centre of the two stars. This position is noted, and from 
it is deduced the angle formed by this line with the meridian. He then 
revolves them a quarter of the circumference, and they are then perpen- 
dicular to their former position. He now separates the wires until the 
one shall exactly bisect one star, while the other wire passes through the 
centre of the second star, reading this distance on the proper scale. He 
has fixed, in these two observations, the position and distance of the two 
components of the double set. — Such is the precision attained in this 
work, that the most minute motions cannot escape detection. If the stars 



154 STRUCTURE OF THE UNIYEESK 

separate from each other at so slow a rate that a million of years would 
be required to perform the circuit of the heavens, their motion would be 
detected in half a year ! 

With machinery more delicate even than this, and better adapted to 
the purpose, and of a kind somewhat different, Bessel once more renewed 
the research after the unattainable parallax of the fixed stars. His great 
instrument, called the heliometer, was mounted as early as 1829, but a 
multitude of causes, and some unsuccessful efforts, delayed his principal 
operations up to August, 1837. Three great principles guided him in his 
selection of 61 in the Swan, as the star on which to perform his observa- 
tions. — First. It was affected by a very great proper motion, a character- 
istic which we will explain fully hereafter, and which indicated it to be 
among the nearest of all the stars. Second. Its duplex character adapt- 
ed it especially to the instrument he was about to employ. Third. 
The region occupied by 61 Cygni contains a number of minute stellar 
points, close to the double star, and presenting admirable fixed points, to 
which the relative motions of the two components of the star to be 
measured might be referred 

With these advantages, and a magnificent instrument, Bessel com* 
menced his observations. He measured the distance from the centre of 
the line joining the two stars, to two of the small stellar points, which 
served him as points of reference, and this kind of observation was re- 
peated night after night, whenever the stars were visible, from the middle 
of August, 1837, up to the end of September, 1838. The entire series of 
observations was then taken and corrected for every possible known error, 
and in case any appreciable change remained, it could only be attributed 
to parallax. 

After a most careful and elaborate investigation, a variation commenced 
to show itself, increasing precisely as parallactic variation ought to in- 
crease, and diminishing as it ought to diminish. The period of these 
changes was precisely a year, and in all particulars, there was an exact 
correspondence in kind with the changes which ought to be produced by 
parallax. But such was their minute character, that Bessell hesitated. 

During another year the observations were repeated. The same results 
came out, and the previous values were confirmed. A third year's ol> 
servations, yielding precisely the same values, removed all doubt, and the 
great Koeningsburgh philosopher announced to the world that he had 
passed the impassable gulf of space, and had measured the distance to the 
sphere of the fixed stars ! But how shall I convey any adequate idea of 
this stupendous distance ? Millions and millions of miles serve only to 
confound the mind. Let us employ a different kind of unit. 

Light, as we have seen, travels with a velocity of 12,000,000 of miles in 
every minute of time. Hence, to reach us from the most remote of all 
the planets, Neptune, whose distance from the sun is about 3,000,000,000 






THE SCALE UPON WHICH THE UNIVERSE IS BUILT. 155 

of miles, will require a journey of about four hours ; but to wing its flight 
across the interval which separates our sun from 61 Cygni, will require a 
period not to be reckoned by hours, or by days, or by months. Nearly 
ten years of time must roll away before its light, flying, in every second, 
192,000 miles, can complete its mighty journey! If the mind revolts at 
this conclusion ; if the distance be too great for comprehension ; if the 
scale of the universe thus suggested even staggers the imagination, I can 
only say, that all subsequent observation has confirmed, in the most 
satisfactory manner, the accuracy of Bessel's results. This great astrono- 
mer first led the way across the mighty gulf which separates us from the 
fixed stars. The distance once passed, the route has become comparatively 
easy, and succeeding observers have determined the parallax of a suffi- 
cient number of stars to show that their results are entirely trustworthy. 

Having now succeeded in gaining a knowledge of the distance which 
separates our sun from its remote companions, we are prepared to extend 
our explorations of the universe. The question naturally arises, how are 
the stars distributed throughout space? — Are they indifferently scattered 
in all directions, or are they grouped together into magnificent systems ? 
A cursory examination of the starry heavens with the naked eye shows 
us, that so far as the large stars are concerned, they do not appear to 
have been distributed in the celestial sphere according to any determi- 
nate law ; but on applying the telescope, that luminous zone which, under 
the name of the Milky Way, girdles the whole heavens, is found to be 
composed of minute stars, scattered like millions of diamond points on 
the deep blue ground of the sky. 

Sir William Herschel conceived the idea that it might be possible to 
fathom this mighty ocean of stars, and to determine its metes and bounds ; 
to give to it figure, and to circumscribe its limits. It will not be difficult 
to explain, in a few words, the general outline of the plan adopted by this 
extraordinary man in the prosecution of this wonderful undertaking. — In 
case we admit that the stars are of equal magnitudes, and at equal dis- 
tances from each other, it would not be difficult to ascertain how far they 
extended in any given direction, the one behind the other. It is mani- 
fest, that in examining the heavens with a telescope of given power and 
aperture, we shall be able to count more stars in the field of view in those 
regions where they are so arranged as to reach farthest back into space ; 
and in case we know their absolute distance from each other, the number 
counted in any field of view, will determine with certainty the length of 
the visual ray reaching to the most remote star visible in that field. 

Now, although the hypothesis that the stars are of equal magnitude, 
and are uniformly distributed through space, may not be rigorously true, 
yet doubtless the mean distances are not far from this hypothesis ; and al- 
though our results may only be approximate, yet as such they are to be 
relied upon, and they become the more interesting as they carry us to the 



M STRUCTURE OF THE UNIVERSE* 

utmost limits of human investigation. Armed with his mighty telescopes, 
Sir William Herschel commenced the stupendous task of sounding the 
heavens, with the purpose of ascertaining whether the stars composing 
the Milky Way were unfathomable, or were bound and circumscribed by 
definite limits. 

Sweeping a circle round the heavens which cut this grand stratum of 
stars in a direction nearly perpendicular to its circumference, he directed 
his great telescope to a certain number of points along this circle, and as 
he moved slowly onward, counted all the stars visible in each field of 
view. It was fair to conclude, that wherever most stars were to be seen, 
there was the stratum deepest. Having gone entirely around the heavens, 
along the circumference of his circle, he had sounded the depth of the 
stars along a section of the Milky Way, and to obtain the figure of 
the section thus cut out was not a difficult matter. 

He assumed a central point on paper to represent his point of observa- 
tion. He then drew from this point lines radiating, and in the actual 
directions which he had given to his telescope while engaged in his ex- 
plorations. On each of these indefinite lines he laid off a distance propor- 
tioned to the number of stars counted in the field of view in the direction 
which the line represented, and by joining these points thus determined, 
he formed a figure which represented the relative depths to which he had 
penetrated into space ; and in case he could be certain that he had gone 
absolutely through the stratum in every instance, and had grasped every 
star, even where 1 the extent was most profound, the figure thus constructed 
would represent the form of the line cut from the outside boundary of the 
Milky Way by the plane of the circle in which the explorations had been 
made. 

Did he then actually penetrate the deepest portions, or any portion, of 
the Milky Way ? This was now his grand question, and to its decision 
he gave all his power and ingenuity. As a unit wherewith to measure 
the space-penetrating power of his telescopes, he assumed the power of 
the human eye, and knowing that stars of the sixth magnitude are within 
the reach of the unaided eye, he concluded, from the law regulating the 
decrease of light, that these minute stars were twelve times more distant 
than the nearest or brightest stars. Now a telescope having an aperture 
such as to concentrate twice as much light as the eye, would penetrate 
into space twice as far, or would reach stars of the twenty-fourth order of 
distances, and so on for telescopes of all sizes. — In this way he concluded 
that his great forty foot reflector, with a diameter of four feet, would 
penetrate 194 times as far as the naked eye, or that it would still see a 
star of the first magnitude if it were carried backward into space 2,328 
times its present distance ! 

Such, then, was the computed length of the sounding line employed in 
gauging these mighty depths. — Suppose, then, it was required to deter- 



THE SCALE UPON WHICH THE UNIVERSE IS BUILT. 1S7 

mine whether this line actually penetrated any given region of the Milky 
Way. Even with a single telescope, a series of experiments may be per- 
formed which go very far to determine tins great question. As the space- 
penetrating power of a telescope depends on the diameter of its aperture, 
it is easy to give to the same instrument different powers, by covering up, 
by circular coverings, certain portions of its object glass. Take circles of 
paste-board, or any other suitable material, and in the first cut an opening 
one inch in diameter, in the second an opening of two inches, and so on, 
up to the diameter of the object glass. These diaphrams being succes- 
sively applied to the object glass, give to the telescope space-penetrating 
powers proportioned to the diameter of the openings. 

In this way Herschel prepared himself to explore one of the deepest 
portions of the Milky Way. The spot selected was a nebulous or hazy 
cloud in the sword handle of Perseus, in which, to the naked eye, not a 
solitary star was visible. I have many times examined the same object, 
which is certainly one of the most magnificent the eye ever beheld. 
With the lowest telescopic aid, many stars are rendered visible, surrounded 
by a hazy light, in which minute glimpse points are occasionally to be 
seen. As the space-penetrating power was increased, the bright spots of 
light were successively resolved into groups of brilliant stars, and more 
nebulous haze came up from the deep distance, indicating that the visual 
ray was not long enough to fathom the mighty distance. At last the full 
power of his grand instrument was brought to bear, when a countless 
multitude of magnificent orbs burst on the sight, like so many sparkling 
diamonds on the deep blue of the heavens. There was no haze behind ; 
the telescopic ray had shot entirely through the mighty distance, and 
the clear deep heavens formed the back-ground of the brilliant picture. 

Thus did Herschel penetrate to the limits of the Milky Way, and send 
his almost illimitable sounding line far beyond, into the vast abyss of 
space, boundless and unfathomable. And now do you inquire the depth 
of this stupendous stratum of stars ? The answer may be given, since 
we have the unit of measure in the distance of stars of the first magnitude. 
Light, with its amazing velocity, requires ten years to come to us from 
the nearest fixed stars, and yet Sir William Herschel concluded, from the 
examinations he had been able to make, that in some places the depth of 
the Milky Way was such, that no less than 500 stars were ranged one 
behind the other in a line, each separated from the other by a distance 
equal to that which divides our sun from the nearest fixed star. — So that, 
for light to sweep across the diameter of this vast congeries of stars, 
would require a period of a thousand years at the rate of 12,000,000 of 
miles in every minute of time ! 

The countless millions of stars composing the Milky Way appear to be 
arranged in the form of a flat zone or ring, or rather stratum, of irregular 
shape, which I shall explain more fully hereafter. Its extent is so great 



158 STRUCTURE OF THE UNIVERSE, 

as properly to form a universe of itself. — If it were possible, to-night, to 
wing our flight to any one of the bright stars which blaze around us, 
sweeping away from our own system, until planet after planet fades in 
the distance, and finally the sun itself shrinks into a mere star, alighting 
on a strange world that circles round a new and magnificent sun, which 
has grown and expanded in our sight, until it blazes with a magnificence 
equal to that of our own, here let us pause and look out upon the starry 
heavens which now surround us. 

We have passed over sixty millions of millions of miles. We have 
reached a new system of worlds revolving about another sun, and from 
this remote point we have a right to expect a new heavens, as well as a 
new earth on which we stand. But no. — Lift up your eyes, and lo ! the 
old familiar constellations are all there. Yonder blazes Orion, with its 
rich and gorgeous belt ; there comes Arcturus, and yonder the Northern 
Bear circles his ceaseless journey round the pole. All is unchanged, and 
the mighty distance over which we have passed is but the thousandth 
part of the entire diameter of this grand cluster of suns and systems ; 
and although we have swept from our sun to the nearest fixed star, and 
have traveled a distance which light itself cannot traverse in less than 
ten years, yet the change wrought by this mighty journey, in the appear- 
ance of the heavens, is no greater than would be produced in the relative 
positions of the persons composing this audience to a person near its 
centre, who should change his seat with his immediate neighbor ! 

Such, then, is the scale on which the starry heavens are built. If, in 
examining the magnificent orbits of the remoter planets, and in tracing 
the interminable career of some of the far-sweeping comets, we feared 
there might not be room for the accomplishment of their vast orbits, our 
fears are now at an end. There is no jostling here ; there is no interfer- 
ence, no perturbation of the planets of one system by the suns of an- 
other. Each is issolated and independent, filling the region of space as- 
signed, and within its own limits, holding on its appointed movements. 

Thus far we have spoken only of the Milky Way. In case it be possi- 
ble to pierce its boundaries, and pass through into the regions of space 
which lie beyond, the inquiry arises, what meets the vision there ? What 
lies beyond these mighty limits? Does creation cease with this one great 
cluster, and is all blank beyond its boundary ? 

Here again the telescope has given us an answer. When we shall have 
traveled outward from our own sun, and passed in a straight line from 
star to star, until we shall have left behind us in grand perspective a series 
of five hundred suns, we then stand on the confines of our own great 
cluster of stars. All behind blazes with the light of countless orbs, scat- 
tered in wild magnificence, while all before us is deep, impenetrable, 
unbroken darkness. No glance of human vision can pierce the dark 
profound. 



THE SCALE OUT WHICH THE UNIVERSE IS BUILT. 159 

But summoning the telescope to our aid, let us pursue our mighty 
journey through space ; far in the distance we are just able to discover 
a faint haze of light — a minute luminous cloud which comes up to meet 
us — and towards this object we will urge our flight. We leave the 
shining millions of our own great cluster far behind. Its stars are shrink- 
ing and fading ; its dimensions are contracting. It once filled the whole 
heavens, and now its myriads of blazing orbs could almost be grasped 
with a single hand. But now look forward. — A new universe, of aston- 
ishing grandeur, bursts on the sight. The cloud of light has swelled and 
expanded, and its millions of suns now fill the whole heavens. 

We have reached the clustering of ten millions of stars. Look to the 
right ; there is no limit ; — look to the left ; there is no end. Above, below, 
sun rises upon sun, and system on system, in endless and immeasurable 
perspective. Here is a new universe, as magnificent, as glorious as our 
own, — a new Milky Way, whose vast diameter the flashing light would 
not cross in a thousand years. Nor is this a solitary object. Go out on 
a clear cold winter night, and reckon the stars which strew the heavens, 
and count their number, and for every single orb thus visible to the naked 
eye the telescope reveals a universe, far sunk in the depths of space, and 
scattered with vast profusion over the entire surface of the heavens. 

Some of these blaze with countless stars, while others occupying the con- 
fines of visible space, but dimly stain the blue of the sky, just percepti- 
ble with the most powerful means that man can summon to the aid of his 
vision. These objects are called clusters and nebulae, — clusters when near 
enough to permit their individual stars to be shown by the telescope, neb- 
ulae when the mingled light of all their suns and systems can only be 
seen as a hazy cloud. 

Thus have we risen in the orders of creation. We commenced with a 
planet and its satellite ; — we rose to the sun and its revolving planets, a 
magnificent system of orbs, all united in«fco one great family, and governed 
by the same great law ; and we now find millions of these suns clustered 
and associated together in the formation of distinct universes, wliose 
number, already revealed to the eye of man, is not to be counted by scores 
or hundreds, but has risen to thousands, while every increase of telescopic 
power is adding by hundreds to their catalogue. 

Let us now explain these "island universes," as the Germans have aptly 
termed them, and attempt approximately to circumscribe their limits, and 
measure their distances from us, and from each other. — Sir William Her- 
schel, to whom we are indebted for this department of astronomy, con- 
ceived a plan by which it was possible approximately to sound the depths 
of space, and determine, within certain limits, the distance and magnitudes 
of the clusters and nebulae within the reach of his telescope. To convey 
some idea of his method of conducting these most wonderful researches, 
imagine a level plane, of indefinite extent, and along a straight line, sep- 



160 STRUCTURE OF THE UNIVERSE. 

arated by intervals of one mile each, let posts be placed, bearing boards 
on which certain words are printed in letters of the same size. The 
words printed on the nearest board, we will suppose, can just be read with 
the naked eye. To read those on the second, telescopic aid is required, 
and that power which suffices to enable the letters to be - dis- 
tinctly seen, is exactly double that of the unaided eye. The tel- 
escope revealing the letters at the distance of three miles is 
three-fold more powerful than the eye, and so of all the others. In this 
way we can provide ourselves with instruments whose space-penetrating 
power, compared with that of the eye, can be readily obtained. 

Now to apply these principles to the sounding of the heavens. The 
eye, without assistance, would follow and still perceive the bright star 
Sirius, if removed back to twelve times its present distance. — After this, as ife 
recedes, it must be followed by the telescope. Suppose, then, a nebula is 
discovered with a telescope of low power, and it is required to determine 
its character and distance. The astronomer applies one power after an- 
other, until he finally employs a telescope of sufficient reach to reveal the 
separate stars of which the object is composed, which shows it to be a 
cluster ; and since the space-penetrating power of this instrument is known, 
relative to that of the human eye, in case the power is one hundred times 
greater than that of the eye, then would the cluster be located in space 
one hundred times farther than the eye can reach, or twelve hundred 
times more remote than Sirius, or at such a distance that its light would 
only reach our earth after a journey of 120,000 years ! 

Such was Herschel's method of locating these objects in space. Some 
are so remote as to be far beyond the reach of the most powerful instru- 
ments, and no telescopic aid can show them other than nebulous clouds of 
greater or less extent. It was while pursuing these g and investigations 
that Herschel was led to the conclusion, that among the nebulae which 
were visible in the heavens, there were some composed of chaotic matter, 
a hazy, luminous fluid, like that occasionally thrown out from comets on 
their approach to the sun. 

Among these chaotic masses he discovered some in which the evidences 
of condensation appeared manifest, while in others he found a circular 
disk of light, with a bright nucleus in the centre. Proceeding yet farther, 
he found well formed stars surrounded by a misty halo, which presented 
all the characteristics of what he now conceived to be nebulous fluid. 
Some of the unformed nebulae were of enormous extent and among those 
partially condensed, such as the nebulae with planetary disks, many were 
found so vast that their magnitude would fill the space occupied by the 
sun and all its planets, forming a sphere with a diameter of more than 
6000 millions of miles. Uniting these and many other facts, the great 
astronomer was finally brought to believe, that worlds and systems of 
worlds might yet be in the process of formation, by the gradual conden- 



THE SCALE UPON WHICH THE UNIVERSE IS BUILT. 161 

sation of this nebulous fluid, and that from this chaotic matter originally 
came the sun and all the fixed stars which crowd the heavens. This 
theory, extended, but not modified, in the hands of Laplace, is made to 
account for nearly all the phenomena of the solar system, and has been 
already referred to in a former lecture. 

For a long time, this bold and sublime speculation was looked upon, 
even by the wisest philosophers, with remarkable favor. The resolution 
of one or two nebulas, (so classed by Herschel), with the fifty-two feet 
reflector of Lord Rosse, has induced some persons to abandon the theory, 
and to attempt to prove its utter impossibility. All that I have to say, 
is, that Herschel only adopted the theory after he had resolved many 
hundreds of nubulse into stars-; and if there ever existed a reason for ac- 
cepting the truth of this remarkable speculation, that reason has been 
scarcely in any degree affected by recent discoveries. 

I have examined a large number of these mysterious objects, floating 
on the deep ocean of space like the faintest filmy clouds of light. No 
power, however great, of the telescope, can accomplish the slightest 
change in their appearance. So distant that their light employs (in case 
they be clusters) hundreds of thousands of years in reaching the eye that 
gazes upon them, and so extensive, even when viewed from such a dis- 
tance, as to fill the entire field of view of the telescope many times. 
Sirius, the brightest, and probably the largest of all the fixed stars, with 
a diameter of more than a million of miles, and a distance gf only a single 
unit, compared with the tens of thousands which divide us from some of 
the nebulas,- and yet this vast globe, at this comparatively short distance, 
is an inappreciable point in the field of the telescope. What, then, must 
be the dimensions of those objects, which, at so vast a distance, fill the 
entire field of view even many times repeated ? 

Herschel computes that the power of his great reflector would follow 
one of the large clusters if it were plunged so deep in space that its light 
would require 350,000 years to reach us, and the great telescope of Lord 
Rosse would pursue the same object probably to ten times this enormous 
distance. 

Such examinations absolutely overwhelm the mind, and the wild dream 
of the German poet becomes a sort of dreadful sublime reality : — 

" God called up from dreams a man into the vestibule of heaven, saying, 
' Come thou hither, and see the glory of my house.' And to the servants 
that stood around his throne he said, w Take him, and undress him from 
his robes of flesh : cleanse his vision, and put a new breath into his nostrils ; 
only touch not with any change his human heart — the heart that weeps 
and trembles.' It was done : and, with a mighty angel for his guide, 
the man stood ready for his infinite voyage ; and from the terraces of 
heaven, without sound of farewell, at once they wheeled away into 
endless space. Sometimes with the solemn flight of angel wing they fled 

U 



162 STRUCTURE OF THE UNIVERSE. 

through Zaarrahs of darkness, through wildernesses of death, that divided 
the worlds of life ; sometimes they swept over frontiers, that were quick- 
ening under prophetic motions from God. Then, from a distance 
that is counted only in heaven, light dawned for a time through 
a sleepy film ; by unutterable pace the light swept to them, they by 
unutterable pace to the light. In a moment the rushing of planets 
was upon them : in a moment the blazing of suns was around them. 

" Then came eternities of twilight, that revealed, but were not revealed. 
On the right hand and on the left towered mighty constellations, that by 
self-repetitions and answers from afar, that by counter-positions, built up 
triumphal gates, whose architraves, whose archways — horizontal, upright 
— rested, rose — at altitude by spans — that seemed ghostly from infinitude. 
Without measure were the architraves, past numbers were the archways, 
beyond memory the gates. Within were stairs that scaled the eternities 
below ; above was below — below was above, to the man stripped of grav- 
itating body : depth was swallowed up in height insurmountable, height was 
swallowed up in depth unfathomable. Suddenly as thus they rode from 
infinite to infinite, suddenly, as thus they tilted over abysmal worlds, 
a mighty cry arose — that systems more mysterious, that worlds more 
billowy, — other heights and other depths, — were coming, were nearing, 
were at hand. 

" Then the man sighed, and stopped, shuddered, and wept. His over- 
(adened heart uttered itself in tears ; and he said — ' Angel, I will go no 
farther. For the spirit of man acheth with this infinity. Insufferable 
is the glory of God. Let me lie down in the grave and hide me from 
the persecution of the infinite; for end, I see there is none.' And from 
all the listening stars, that shown around issued a choral voice, 'The man 
speaks truly : end there is none, that ever yet we heard of.' ' End is 
there none ? ' the angel solemnly demanded : 4 Is there indeed no end ? — 
and is this the sorrow that kills you ? ' But no voice answered, that he 
might answer himself. Then the angel threw up his glorious hands to 
the heaven of heavens, saying, 'End is there none to the universe of God. 
Lo ! also there is ^.beginning.' " 



LECTURE X. 

THE MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 

Having reached, in the course of the preceding lecture, to the outer- 
most confines of the visible creation, let us now return home from this 
survey of the " island universes " which crowd the illimitable regions of 
space, to the stars which compose our own cluster, and learn how far the 
human mind has progressed in its examination of the millions of suns 
which constitute, in a more definite sense, our own Milky Way. 

We have already seen that the parallax of 61 Cygni rewarded the 
laborious and extraordinary efforts of Bessel. The example set by 
this great astronomer encouraged those who followed him, and while 
his results in this particular case had been confirmed in the most astonish- 
ing manner, the distances of many other stars have been obtained, until 
a sufficient amount of data has been accumulated to determine the 
approximate distances of the sphere of the fixed stars of different mag- 
nitudes. Struve estimates the mean distance of stars of the first magni- 
tude to be 986,000 times the radius of the earth's orbit, or so remote that 
their light reaches us only after a journey of fifteen years and a half. 
Stars of the second magnitude send us their light in twenty-eight years, 
those of the third magnitude in forty-three years ; while the light from 
stars of the ninth magnitude only reaches the eye of the observer after 
traversing space for five hundred and eighty-six years, at the rate of 
twelve millions of miles in every minute of time. 

My range of investigation does not permit me to explain, at this time, 
how these extraordinary conclusions have been reached, The reasoning, 
however, is close and clear, and the results are no doubt approximately 
correct. 

Such, then, are the distances separating man from the objects of his 
research. To have attained to a knowledge of these distances even, is 
sufficiently wonderful, but what we are about to reveal as the results of 
human investigation among these far distant orbs, cannot fail to fill the 
mind with astonishment, and demonstrate the great truth that "man has 
been made but a little lower than the angels." 

Before it became possible to examine with absolute certainty the places 
of the stars, with a view to ascertain their absolute fixity, many difficult 
preliminary preparations had to be accomplished. Instruments of the 
most perfect kind must be provided, not only in their optical perform- 



164 STRUCTURE OF THE UNIVERSE. ' 

ances, but in their space-dividing machinery. Moreover, the places of 
the stars, as determined by the best telescopes, must be corrected for 
every possible instrumental error. The two points to which the stars 
are referred are the north pole and the vernal equinox. In case any 
motions belong to these points, their amounts and directions must be 
ascertained and allowed for. Then the effects of refraction, and of the 
abberration of light, were indispensable to a perfect investigation of the 
absolute places of the stars. 

All these and many other preliminary matters having been satisfac- 
torily determined, it became possible to examine, in the most critical man- 
ner, the places of the stars, and to learn whether indeed, (as had been 
supposed for thousands of years), their configurations were eternal and 
unchangeable, or whether they moved among themselves with a motion 
rendered so slow by their immense distance, as hitherto to have escaped 
the most scrutinizing watch. 

Fully armed with the necessary instruments, it did not require many 
years to determine the grand truth, that among the tens of thousands of 
stars which fill the heavens, not a solitary one, in all probability, is in a 
state of absolute rest. Many were found to move so swiftly, that their 
velocity was determined even in a single year; while others, in conse- 
quence of their enormous distance, may require centuries to detect any 
appreciable change. In the outset these extraordinary movements seemed 
to be directed by no law — some stars were sweeping in one direction, 
and some in another. Motion, ceaseless, eternal motion, seems to be 
stamped on the entire universe, and while the stars are pursuing their 
mighty orbits, we cannot resist the idea that our own sun, the centre of 
our great planetary system, itself a star, must participate in the general 
movement, and is, in all probability, urging its flight, accompanied by all 
its planets, satellites, and comets, to some unknown region of space. 

The revolution of the stars, the organization of the grand cluster with 
which our sun is associated, the demonstration of the sun's absolute trans- 
lation through space, its direction, velocity, and period, are the topics to 
which I invite your attention in the closing lecture of the present course. 

When forced to acknowledge the rotation of our globe on its axis, and 
its swift orbitual motion, surrounded by wheeling planets and flying 
comets, the mind naturally retreats to the sun as the great immovable 
centre, where it can rest and contemplate these circling worlds. But 
even here, as we shall presently see, there is no rest. The sun himself be- 
comes a subordinate member of a grander combination of worlds, and, 
obedient to higher influence, sweeps around in its unmeasured orbit. 

We shall present a rapid summary of the evidence of change among 
the fixed stars, and then proceed to develope the reasoning by which the 
direction and velocity of the sun's motion in space has been determined. 

More than two thousand years ago, the celebrated Greek astronomer, 



THE MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 165 

Hipparchus, was astonished by the sudden bursting forth of a brilliant 
star in a region of the heavens where none had previously existed. Up 
to this time, no doubt of the immutability of the starry sphere seems to 
have been entertained, and while the philosopher gazed and wondered, he 
resolved to execute a work from which posterity might learn the change 
of the celestial sphere. He undertook and completed his great catalogue 
of the places of a thousand stars, locating them with all the accuracy per- 
mitted by the rude instruments then in use. Subsequent observers, by 
comparing their own determined positions of the stars with their places 
as fixed on the catalogue of Hipparchus, could readily perceive any sen- 
sible change which might occur in their configuration, the appearance of 
new stars, or the disappearance of those which had once existed. 

The sudden breaking forth of a new star is a phenomenon of such 
wonderful character that we might well doubt the possibility of its occur- 
rence, if we were obliged to rely on the historioal account transmitted to us 
from the time of Hipparchus. But, fortunately, more than one brilliant 
example of the kind has occurred in modern times, presenting the most 
unequivocal evidence of the reality of this inexplicable wonder. 

In 1572, a new star of great splendor appeared suddenly in the constel- 
lation Cassiopeia, occupying a position which had previously been blank. 
This star was first perceived by Schuler, of Wittemburg, on the 6th of 
August. It was detected by Tycho, the Danish astronomer, on the 11th 
of the following November, and the wonder produced by this most extraor- 
dinary phenomenon induced him to give to the star the most unremit- 
ting attention. Its magnitude increased until it is said to have surpassed 
even Jupiter in splendor, and finally became visible in the day-time. It 
retained its greatest magnitude but for a very short time, when it com- 
menced to diminish in brilliancy, changing from white to yellow, then to 
reddish, and finally it became faintly blue ; and so diminishing by de- 
grees, it vanished from the sight in March, 1574, and has never since 
been seen. 

In the year 1604, while the scholars of Kepler were engaged in obser- 
vations of Mars, Jupiter and Saturn, -then in close proximity to each 
other, having been interrupted a day or two by clouds, on the return of 
fine weather, Maestlin was astonished to find near the planets then in the 
constellation Ophiuchus, a brilliant star, which certainly had not been 
there a few days before. This object attracted the attention of all the 
great astronomers then living, and was particularly observed by Galileo 
and Kepler. It is said to have attained a splendor equal to that of the 
planet Venus, and from this, its greatest brilliancy, it gradually declined, 
until, about the beginning of 1606, it ceased to be visible, and no tele- 
scopic power has since been able to detect any star in the place once oc- 
cupied by this remarkable stranger. 

Although observedwith the greatest care, no sensible parallax was ever 



166 STRUCTURE OF THE VXIVERSE. 

detected in either of these objects, and no doubt exists as to their occupy. 
ing the region of the fixed stars. Many other less remarkable examples 
are on record, but up to the present no satisfactory explanation of this 
astonishing phenomenon has been given, Whether it indicates the actual 
destruction of some magnificent system, or the revolution of these stars 
in orbits of great eccentricity, causing them to appear to us, like the com- 
ets, only in the perihelion points of their mighty orbits, is equally un- 
certain. One thing is certain : they present evidence of change in the 
starry heavens, of the most startling and irresistible kind. 

While new stars have occasionally made their appearance, to astonish 
mankind with their brilliancy, there are many well authenticated cases 
of the entire disappearance of old stars, whose places had been fixed with 
a degree of certainty not to be doubted. — In October, 1781, Sir William 
Hershel observed a star, No. 55 in Flamsted's catalogue, in the constel- 
lation Hercules. In 1790, the same star was observed by the same as- 
tronomer, but since that time no search has been able to detect it. The 
star is gone ; whether never to return, it is impossible to say. A like dis- 
appearance has occurred with reference to the stars numbered 80 and 81, 
both of the fourth magnitude, in the same constellation. In May, 1828, 
Sir John Herscchel missed the star numbered 42, in the constellation 
Virgo, which has never since been seen. Examples might be multiplied, 
but it is unnecessary. 

In these cases the stars have been lost entirely ; — no return has ever 
been marked ; and but for the discovery of another class of remarkable ob- 
jects among the stars, no return would probably ever have been suspect- 
ed. If I could direct your attention to-night to a brilliant star named Al- 
gol, in the head of Medusa, and bring a powerful telescope to aid in your 
examinations, this star, while you are watching it, might be seen to lose its 
splendor, and from its rank of the second magnitude to decline in bright- 
ness, until it would scarcely be visible to the naked eye. Having reached 
a certain limit, it would commence an increase, and by slow degrees re- 
sume its original splendor. — This decrease and increase is actually accom- 
plished in about eight hours. Having regained its usual light, it remains 
stationary for about two days and a half, and then repeats the changes al 
ready detailed ; and thus have its periodical fluctuations continued since 
the date of its discovery, with the most astonishing regularity. The bright 
star marked Beta, in the constellation Lyra, is known to pass from the 
third to the fifth magnitude, and to regain its light in a period of six days 
and nine hours. These are called periodical stars and a sufficient number 
have already been detected to present a progressively increasing series of 
periods from two days twenty hours up to four hundred and ninety-four 
days, and in one case even many years. 

Here, again, are phenomena indicative of extraordinary activity in these 
remote regions of space. — No explanation of these changes ha^ yet been 



THE MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 167 

given in all respects satisfactory. Some have attributed them to the ex- 
istence of dark spots on the stars, which, by rotation on an axis, periodic- 
ally present themselves, and thus dim the lustre of the stars. Others think 
the changes are due to the revolution of large planets about the stars 
which, by coming between the eye and the star, eclipse a portion of its 
light; while a third class conceive the fluctuations to arise, in some in- 
stances at least, from an orbitual motion of the stars in orbits of excessive 
elongation, and so located as to have their greater axes directed towards 
our system. 

It will be seen that this theory may be readily extended so as to em- 
brace the new stars already referred to, and even to account for those 
which have been lost from their places in the heavens. Here, however, 
we enter the confines of the uncertain. Centuries may roll away before 
the true explanation of these astonishing changes shall be given ; but the 
mind is on the track, and with a steady and resistless movement is slowly 
pushing its investigations deeper and still deeper into the dark unknown. 

While the phenomena of the new and lost stars, and the fluctuations in 
the light of the variable ones, gave undeniable evidence of constant change 
in what Aristotle was pleased to call the eternal and incorruptible heavens, 
Herschel's brilliant discovery of the orbitual motion of the double star? 
gave to the mind the opportunity of determining the nature of the law 
which sways the movements in these distant regions of space. It was nat- 
ural, in the first efforts to compute the orbits of the double stars, to adopt 
the hypothesis that they attracted each other by the same law which pre- 
vails in the planetary system. Results did not disappoint expectation. — 
Gravitation, which Newton, in the outset of his great discovery, had bold- 
ly affirmed exerted its influence wherever matter existed or motion 
reigned, was extended, in the most absolute manner, to the region of the 
fixed stars. There, at a distance from our own system almost inconceiv- 
able, suns and systems of suns, rising in orders of greater complexity, re- 
volving with swift velocity, or with slow and majestic motion, bore testi- 
mony, ample and unequivocal, to the truth of the great law of universal 
gravitation. 

Every particle of matter in the universe attracts every other particle 
of matter with a force which is proportioned directly to the mass, and 
which decreases as the square of the distance at which it operates increas- 
es. This is no longer a bold hypothesis. The double star marked Zeta, 
in the constellation Hercules, has been subjected to the analysis of the 
computer. The elements of its orbit have been obtained, and true to its 
predicted period, it has actually performed an entire revolution in a period 
of thirty-five years. The components of the star Eta, in the Northern 
Crown, revolve around their common centre in about forty-four years. 
Both of these pairs have completed an entire revolution since their discov- 
ery. Many others might be named, but my only object, at present, is to 



68 STRUCTURE OF THE UNIVERSE. 

exhibit the evidence which shall remove all doubt as to the actual exten 
sion of the law of gravitation to the fixed stars. 

Let it be remembered that this department of astronomy is yet in its 
infancy. Thousands of double stars have been detected, and every year 
adds hundreds to the list. Among these, a large proportion must prove 
to be binary systems, varying in their periods of revolution, from thirty 
years or less, up to many thousands, perhaps millions of years. 

The association of two suns naturally suggests the possible union of a 
greater number, forming more complicated systems. This idea has been 
verified — a large number of triple systems has been discovered. In a few 
instances quadruple sets have been found, of which a remarkable example 
exists in "the constellation of the Harp. Here was found four suns, arranged 
in pairs of two. The components of the first pair revolve around each 
other in about one thousand years ; those of the second pair appear to 
require about double that period, while one pair revolves about the other 
in a period which, determined roughly from their distance, cannot fall 
much below a million of years ! The evidence of the physical union of 
these four stars into one grand system rests, at present, on the ascertained 
fact that their proper motions are the same. 

From quadruple systems we rise, by analogy, still higher, until we find 
hundreds, sometimes thousands, of stars compacted together in so small a 
compass that their proximity cannot be the effect of accident. Look at 
the beautiful little cluster called the Pleiades : an ordinary eye may here 
see six or seven stars. One of very great power has been known to count 
fourteen in this group, while the telescope increases the number to hun- 
dreds ; and yet the space in which they are located might easily be cov- 
ered by the moon. 

Suppose an indifferent scattering of the stars through space, and com- 
pute the chances that such a number would fall together at any one point, 
and we shall find not one chance out of millions in favor of such an acci- 
dent. We are therefore forced to the conclusion that here is a more 
magnificent order, one in which hundreds of suns, surrounded by their 
subordinate worlds, are all united by gravitation into one grand system 
This is not a solitary example. — Many of these beautiful objects, compar- 
atively close to our sun, are found in the heavens, leading the mind grad- 
ually up to the contemplation and examination of that mighty system 
of systems, that great cluster of clusters, the Milky Way, of which all these 
are but subordinate groupings, — vast in themselves, but when compared 
with the whole, mere units among the millions of which it is composed. 

From what we have seen, it is impossible to avoid the conclusion that 
'gravitation exerts its power among the myriads of shining orbs which 
strew the Milky Way. The innumerable suns which form this stupen- 
dous cluster must feel the reciprocal influence of each other, and nothing 
short of the centrifugal force arising from orbitual motion can balance 



THE MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 169 

this universal attractive power, and give to this grand system the great 
characteristic of stability. 

Herchel succeeded, at least approximately, in sounding the profundities 
of the Milky Way, and fixed the relative position of our own sun among 
the stars by which it is surrounded. He found it to be located not very 
distant from the centre of the great stratum and near the line where the 
principal current of stars divides into two great streams, which for a time 
separate from each other, but finally reunite in a distant region of the 
heavens. 

Having accomplished thus much, this great astronomer attempted the 
resolution of the grand problem of the sun's movement through space. 
This investigation is so lofty, so daring and utterly incomprehensible at 
the first glance, that its mere announcement produces little effect on the 
mind. Consider, for one moment, what it involves. Man is located on a 
planet almost infinitely larger than himself. This planet is swiftly revolv- 
ing on its axis, and in its orbit round a great central luminary, the sun. 
The daring philosopher participates in all these motions. He provides 
himself with instruments which measure the distances and positions of 
the almost infinitely distant fixed stars. These fixed stars, when sub- 
jected to his critical examination, cease to be fixed, and are found to be 
moving with astonishing velocity in all directions. Among these he num- 
bers his own sun, and although borne along in the progressive motion of 
his own great centre, he ventures to attempt the determination of the fact 
of its actual motion, the direction in which it moves, and the velocity 
with which it is sweeping through space. 

This problem is so wonderful that I beg your earnest attention while 
the effort is made to simplify the reasoning by which its resolution has 
been accomplished. 

Before the actual motions of the earth were discovered, the sun, moon, 
and planets, as well as the stars, appeared to move in certain directions, 
and with certain velocities, not easily explained. The rotation of the 
earth on its axis rendered a clear explanation of the diurnal movements 
of the heavenly bodies, and its orbitual motion around the sun explained 
the sun's apparent annual movement among the fixed stars. Thus it is 
seen and readily apprehended, that in case the spectator is progressing, 
his actual motion may be transferred to distant bodies under examina- 
tion, and these may appear to move while he seems to be at rest. 

Now in case the sun is sweeping towards any quarter of the heavens, it 
must carry with it all its planets, satellites, and comets. The earth is 
borne along in common with its companions, and the observer on its sur- 
face will transfer his own movement through space to the distant objects 
which only appear to change their places, in consequence of his own trans- 
lation through space. Thus the distant stars may be affected with a par- 
allactic change, not to be confounded with that produced by the revolu- 



170 STRUCTURE OF THE UNIVERSE. 

tion of the earth in its orbit, but occasioned by the fact that while the 
earth revolves around the suu, she is carried forward by this luminary in 
his journey through space. As the whole system participates in this mo- 
tion, in case the planets are inhabited, their astronomers will detect in 
the fixed stars the parallactic motion due to the sun's movement, and 
hence this change among the stars may be properly termed their systematic 
parallax. 

Herschel commenced his examination of this great problem by forming 
a catalogue of stars situated in all parts of the heavens, in which an ap- 
preciable amount of proper motion had been detected and measured. Now 
in case this apparent motion of the stars could be attributed to the move- 
ment of the solar system through space, a close scrutiny of the directions 
in which the stars appeared to move would indicate the direction in which 
the observer, carried along with the sun, was passing through space. 

In case a person is travelling on a railway, in a direct line through a 
forest of trees, as he advances, all objects towards which he is moving will 
appear to open out or separate from each other, while those left behind 
will appear to close up. If, then, the astronomer, borne along by the 
movement of the sun through the vast forest of stars by which he is sur- 
rounded, desires to ascertain the direction in which he is progressing, let 
him search the heavens until he finds a point where the stars seem to be 
increasing their distance from each other. Should he find such a point, 
let him confirm his suspicions by looking in the direction precisely oppo- 
site and behind him, and in case he finds the stars located in this region 
closing up on each other, he may fairly conclude that he has found the 
direction in which he is moving, and a rigid coincidence of all the phe- 
nomena would demonstrate the accuracy of his conclusions. 

Such was the general train of investigation adopted by Herschel. 
After as extended an examination as the data with which he was then fur- 
nished permitted, he announced his belief that a part of the proper mo- 
tion of the fixed stars must be attributed to the effect of systematic par- 
allax, and that the solar system was moving through space towards a point 
in the constellation Hercules. 

The announcement of this astonishing result was received with hesita- 
tion and doubt by the best living astronomers, and Herschel died before 
any confirmation of his great theory had been obtained. After his death, 
for nearly half a century, no mind seemed willing to renew the investiga- 
tion. The theory fell into disrepute, and was only regarded as a bold 
and sublime speculation, but not founded on any well determined obser- 
vations. 

Within a few years, the problem has engaged the attention of the dis- 
tinguished astronomers of Russia. Argelander, of Bonn, led the way, and 
by a train of reasoning based upon extensive and accurate observations, 
has sustained and demonstrated, in the most undeniable manner, not only 



THE MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 171 

the general truth of Herschel's theory, but has even confirmed the direc- 
tion in which that astronomer believed the solar system to be moving. 

Here again permit me to attempt a popular explanation of Argelander's 
reasoning. Suppose a single star to have its place fixed absolutely 
by observation on the first day of the year 1700. One hundred years 
after, its place is again determined, when it is found to have shifted its 
position. Conceive the star to have so moved as to reach the meridian 
earlier than it formerly did. When on the meridian, its old place will 
be behind or east of the new place, and a line joining the old and new 
places will show the direction in which the star has been moving, and the 
distance between the two places will exhibit the amount of motion in one 
hundred years. If the star do not move exactly north or south, its line 
of direction will form an angle with the meridian, whose value is deter- 
mined from a comparison of the old and new places of the star. 

Argelander commenced by selecting five hundred stars, in all regions 
of the heavens, whose places had been well determined by preceding as- 
tronomers. The preference was of course given to those which had been 
longest subjected to observation. Having himself determined the new 
places of all these stars, a comparison of his own with previously observed 
positions determined the direction in which these stars were moving, and 
their rates of motion. The angles formed by the lines along which each 
star was progressing, with the meridian, became known from observation, 
and these angles we shall call the observed angles of direction. Now it is 
not difficult to compute the directions in which the stars would appear to 
move, if their motion be produced by the movement of the solar system. 

Suppose, for example, that the sun, with its planets, is sweeping exactly 
towards the north pole of the heavens, then would all the stars appear to 
move towards the south. Those in the equator would move with the 
swiftest velocity from the north pole, but those nearest the pole would 
appear to separate from each other, while their recess from the pole would 
be comparatively slight. To render this reasoning still plainer, imagine 
this room to be pierced on every side, so that an eye placed at the centre 
could see every star in the heavens through the openings. Through each 
of these holes conceive iron rods to pass, all meeting at a point in the cen- 
tre, and all directed exactly to the stars. On the outside let golden balls 
be fixed to the extremities of these rods, to represent the stars. Now, 
grasping the extremities of all these rods in the hand, urge the point 
where they all unite towards the north pole, and watch the movement of 
the balls at the outer extremities of the rods. The ball corresponding to 
the north star will scarcely seem to move, because the eye travels directly 
towards it. The balls corresponding to the stars on the equator, having 
their rods perpendicular to the direction of the motion of the central 
point will sweep swiftly towards the south. The idea once gained, there 
is no difficulty in its application. 



172 STRUCTURE OF THE UNIVERSE. 

The visual rays drawn to the stars correspond to the rods, and these 
rays, meeting in the eye of the observer, are carried forward by the sun 
in its progression through space. I have supposed the system to move 
due north ; but in case the motion be assumed in any other direction, it 
is easy to compute the changes consequent. Understanding these pre- 
liminary statements, we are prepared to follow Argelander in his investi- 
gation. 

The five hundred stars selected for examination were divided into three 
groups, according to the amount of annual proper motion. The first con- 
tained only such stars as were seen to move with a velocity not less than 
one second of space in a year. Although this motion may appear exces- 
sively slow, yet its direction in one hundred years may be determined 
with very great precision. A general examination of the direction in 
which the stars of this first group appeared to move, indicated the quarter 
of the heavens towards which the solar system must be progressing ; and 
now commenced the investigation, having for its object the discovery of 
the exact point. — To accomplish this, a point was assumed, and on the 
hypothesis that it was correctly chosen, the directions of the motion of all 
the stars composing the first group were computed, and the angles formed 
by their lines of direction with the meridian were determined. 

If the motion of these stars was the effect of systematic parallax, and 
if the direction of the solar movement had been accurately chosen, then 
would the computed angles of direction agree exactly, in every instance, 
with the observed angles of direction. The comparison of these angles 
having been made, it was easy to see the discrepancies, and by shifting 
the assumed point, these differences could be reduced to their minimum 
value. The point which gave the smallest differences between the ob- 
served and computed angles would be the one towards which the solai 
system was progressing. Such was the reasoning of Argelander, and 
such the train of investigation on which he relied for the resolution of this 
great problem. 

Having closed his examinations based on the group of stars with the 
most rapid motion, and having found the point in the heavens which cor- 
responded to their motions, he proceeded to execute his calculations with 
reference to his second group. The stars of this group moved annually 
an amount greater than half a second of space, and less than one second. 
The result was again reached, and direction of the solar motion thus 
derived, agreed, in a remarkable manner, with that obtained from the 
first group. A further confirmation was obtained by executing the calcula- 
tion founded on the motions of the third and last group into which he had 
divided his five hundred stars. — The final result settled, probably forever, 
the grand fact that the sun, with its entire cometary and planetary sys- 
tem, is sweeping through space towards a point whose place must fall 
somewhere within the circumference of a circle whose diameter is about 
equal to four times that of the moon. 



THE MOTIONS AND REVOLUTION S OF THE FIXED STARS. 173 

The reality of the solar motion once determined, astronomers have not 
been wanting to verify and extend this wonderful examination. Arge- 
lander's results have been confirmed by the investigations of M. Otho 
Struve, the son of the distinguished director of the Imperial Observatory 
of Pulkova; and if, on any fair night, you direct your eye to the constella- 
tion Hercules, and select from its stars the two marked on the globe with 
the Greek letters ir and p on the line joining these stars, and at a distance 
from ir equal to one-quarter of the distance which divides the stars will 
be found the point towards which the sun was directing his course in the 
year 1840. 

Having obtained the direction of the solar motion, we proceed to in- 
vestigate its actual volocity. How swiftly does the sun, with its retinue 
of worlds, sweep onward through space ? It will not be possible to present 
here even an outline of the reasoning of Struve in the resolution of this 
intricate question. — Two points are involved. The determination of the 
annual angular motion of the sun, as it would be seen by a spectator 
situated at a distance equal to that of the stars of the first magnitude. 
This being determined, the angular motion can readily be converted in- 
to linear velocity, in case the mean distance of the stars of the first mag- 
nitude can be satisfactorily obtained. After an elaborate investigation, 
guarded by every care, and open, as it would appear, to no well founded 
objections, M. Otho Struve has finally resolved the first of these wonder- 
ful questions. It is curious to see how nearly the results agree, which 
were obtained from data entirely different, and in no way dependent on 
each other. 

By an examination based on observed right ascensions of the stars, he 
finds that the space passed over by the sun in its progressive movement 
through the heavens, seen from the mean distance of the stars of the first 
magnitude, is three hundred and twenty-one-thousandths of a second of 
arc. The result obtained from observed declinations gave for the same 
quantity three hundred and fifty-seven-thousandths of one second of arc. 
Here is a difference amounting to only thirty-six-thousandths of a second, 
a quantity exceedingly small, when we consider the extraordinary difficul- 
ty of the investigation. 

Let us now convert these members into intelligible quantities. In case 
the sun be supposed to be revolving about some mighty centre, at a dis- 
tance equal to the mean distance of stars of the first magnitude, the period 
necessary to accomplish its stupendous revolution will be 3,811,000 years ! 

Vast as this period appears, we shall see hereafter that we have no right 
to suppose that the centre about which the solar system is revolving, can 
be located at a distance nearly so small as the mean distance of the larger 
stars. But what is the actual velocity ? — How many miles does this mighty 
assemblage of flying worlds accomplish in its unknown journey in every 
year? This is the last question, and even this has not escaped the suq- 



174 STRUCTURE OF THE UNIVERSE. 

cessful examinations of the human mind. The discovery of the parallax 
of one or two fixed stars has already been referred to. — Within a few 
months, an elaborate work, by Struve, on the Sidereal Heavens, has reached 
us, containing some remarkable investigations on the mean distances 
of the stars of the various magnitudes. 

Struve, by a most ingenious and powerful train of investigation, obtains 
a series representing the relative mean distances of the stars of all magni- 
tudes, up to the most minute visible in Herschel's twenty feet reflector. 
From the snn, as a centre, he sweeps successive concentric spheres, between 
whose surfaces he conceives the stars of the several magnitudes to be in- 
cluded* The radius of the first sphere reaches to the nearest stars of the 
first magnitude ; that of the second sphere extends to the farthest stars of 
the same magnitude, and the means of these two radii will be the mean 
distance of the stars of the first magnitude. The same is true with refer- 
ence to the concentric spheres embracing within their surface the stars of 
the various orders of brightness. 

Having, from his data, computed a table exhibiting the relative distances 
of the stars of the different magnitudes, an examination of these figures 
revealed the singular fact that they constituted a regular geometrical pro- 
gression ; and having assumed the distance of the stars of the sixth mag- 
nitude as the unit, the distance of the stars of the fourth magnitude will 
be one-half] that of those of the second magnitude will be one-quarter, and 
so to the even numbers expressing magnitude ; while the distance of the 
stars of the fifth magnitude is obtained by dividing unity by the square 
root of the number 2, and from this the distance of the odd magnitudes 
come by dividing constantly by 2. In mathematical language, the dis- 
tances of the stars of the various magnitudes form a geometrical progres- 
sion whose ratio is equal to unity divided by the square root of 2. 

Having thus obtained the relative mean distances of the stars, in case we 
can find the absolute mean distances of those of any one class, that will 
reveal to us the absolute mean distances of the stars of every class. For 
the approximate accomplishment of this last great object, we are again in- 
debted to the astronomers of Russia. As early as 1808, M. Struve, then 
of Dorpat, attempted the determination of the parallax of a large number 
of stars, and obtained results so small that, in the state of astronomical 
science as it then existed, no confidence could be placed in them. The 
final value of the numerical co-efficient of the aberration of light had not 
been then absolutely determined. Subsequent investigations by Struve 
and Peters have fixed this quantity, and the actual determination of the 
parallax of eight stars recently, has shown that confidence may now be 
placed in the results obtained by Struve nearly 25 years ago. 

By combining all the results, M. Peters finds no less than thirty-five 
stars whose parallaxes have now been determined, either absolute or rela- 
tive, with a degree of accuracy which warrants their employment in in 






THE MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 175 

vestigatiug the problem of the mean parallax of stars of the second" mag- 
nitude. Excluding from this number the stars 61 Cygni, and No. 1830 of 
the Grombridge catalogue, on account of their great proper motion, there 
remained thirty-three stars to be employed in the investigation. 

From a full and intricate examination of all the data, by a process of 
reasoning which I will not attempt to explain at this time, M. Peters finds 
the mean parallax of stars of the second magnitude to be equal to 116 thou- 
sandths of one second of arc, with a probable error less than a tenth part 
of this quantity. Returning now, with this absolute result, to the table of 
the relative distances of the fixed stars of different magnitudes, it is easy 
to fix their absolute distances, as far as confidence can be placed in this 
first approximation. "We find the stars of the first magnitude to be located 
between the surface of two spheres, whose radii are respectively nine hun- 
dred and eighty-six thousand times the radius of the earth's orbit, and one 
million two hundred and forty-six thousand times the same unit. We will 
express the distance in terms of the velocity of light, as no numbers can 
convey any intelligible idea. Stars of the first magnitude send us their 
light in about seventeen } T ears ; those of the second magnitude in about 
thirty years ; — stars of the third magnitude send their light in about forty- 
five years ; those of the fourth magnitude in sixty-five years ; those of the 
fifth in ninety years ; those of the sixth magnitude, the most remote visi- 
ble to the naked eye, send us their light after a journey through space of 
one hundred and thirty years ! while the distance of the lowest order of 
telescopic stars visible in Herschel's twenty feet reflector is such, that their 
light does not reach the eye for 3,511 years after it starts on its tremendous 
journey ! 

Let it be remembered that these results are not conjectures. Though 
they are first approximations to the truth, they are reliable to within the 
tenth part of their value, and are thus far certain ; they raise, in the most 
astonishing manner, our views of the immensity of the universe, and of 
the powers of human genius which have fathomed these vast and over- 
whelming profundities. 

Let us now return to the examination of the absolute amount of pro- 
gressive motion of our sun and system through space. As already stated, 
M. Otho Struve determined its yearly angular motion, as seen from the 
more distant of the stars of the first magnitude. To convert this angular 
motion into miles, a knowledge must be obtained of the absolute mean 
distance of the stars of the first magnitude. This has been accomplished 
by M. Peters, and combining the researches of Argelander, Struve, and 
Peters, we are now able to pronounce the following wonderful results. — 
The sun, attended by all its planets, satellites, and comets, is sweeping through 
space towards the star marked ir in the constellation Hercules, with a velocity 
which causes it to pass over a distance equal to thirty-three millions three hun- 
dred and fifty thousand miles in every year ! 



176 STRUCTURE OF THE USIVERSE. 

And now do you demand how much reliance is to be placed on this be- 
wildering announcement? I answer, that as to the reality of the solar 
motion, there is but one chance out of four hundred thousand that astron- 
omers have been deceived. We cannot resist the evidence, and startling 
as the truth appears, we are obliged to yield our assent, reluctant though 
it may be, to the logical reasoning by which this magnificent result has 
been demonstrated. 

But whither is our system tending ? If moving onward with such tre- 
mendous velocity, is there not danger that ere long it may reach the region 
of the fixed stars, and by sweeping near to other suns and systems, derange 
the order of the planetary worlds ? Let us examine this question for one 
moment, on the hypothesis that the sun alone is moving among all the stars 
of heaven, and that it will hold on in its present direction until it shall reach 
the star in Hercules, towards which it is now urging its flight. This star 
is of the third magnitude, and according to our statement already made, 
the mean distance of its class is such, that its light does not reach "us in a 
period less than forty-six years. Executing the calculation, we find that 
in case the solar system should continue to progress towards that star, it 
cannot pass the enormous interval, even at 33,550,000 miles per annum, in 
less than 1,800,000 years ! 

If the eye of any superior intelligence can behold this amazing scene, 
how stupendous must be the spectacle presented ! In the centre the sun, 
blazing with splendor, pursues its majestic career; — around it roll the 
planets, and about it cluster ten thousand fiery comets. Worlds bright 
and beautiful hover near the sun, — worlds fiery and chaotic seek this great 
centre with impetuous velocity, and then dash away into the farthest range 
of their grand revolution. But the monarch moves on, and his magnificent 
cortege, performing his high behests, follow whithersoever he leads through 
space ! 

Here we reach the boundary which divides the known from the unknown. 
Steadily we have pursued the human mind as it has moved on in its grand 
researches of the universe of God. Time, and space, and number, and dis- 
tance, have all been set at defiance. No limits have been sufficiently great 
to circumscribe its movement. For more than six thousand years, onward ! 
has truly been the word. And here I might very well pause, and rest 
content in the exhibition of the absolute and actual triumphs of human 
genius ; but as the rays of the rising sun penetrate the darkness of night, 
and scattering the gloom, dimly reveal the scenes of earth which are soon 
to be flooded with splendor, so the light of human knowledge breaks over 
the boundaries which divide the known from the unknown, and faintly 
reveals what yet lies far beyond in the dark profound. 

G aided by this light, we shall ask your attention to one of the most 
sublime speculations to which the mind of man has ever risen. I refer to 
the supposed discovery of the great centre about which it is presumed the 
myriads of stars composing our mighty Milky Way are all revolving. 



THE MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 177 

M. Maedler, the author of the recent investigations with reference to 
the Central Sun, has long been known to the astronomical world as the 
successor of M. Struve in the direction of the observatory at Dorpat. His 
computations of the orbitual movements of the double stars have given to 
him a deservedly high celebrity, and the great theory which he has pro- 
pounded is only given to the world after a long and patient examination 
extending through seven years. 

The extension of the law of gravitation to the fixed stars, now absolutely 
demonstrated in the revolutions of the binary systems, settles forever the 
fact, that in the grand association of stars composing our cluster, or, as we 
shall hereafter call it, our astral system, there must be a centre of gravity, as 
certainly as there is one to the solar system. In the organization of the 
solar system we find a central body of vast size, surrounded by small and 
subordinate satellites. Again, among the planets, we find their magni- 
tude very great, when compared with the moons which circulate around 
them. Extending this analogy, early astronomers conceived that this 
principle of a great central preponderating globe would, in all probability, 
obtain in all the higher orders of physical organization. 

This idea, apparently so well founded, was entirely destroyed by the 
discovery of the binary stars. Here we find the next higher organization 
above our solar system, but instead of finding in the bodies thus united a 
vast preponderance in magnitude of one over the other, there are many 
examples in which the two suns thus united b}^ gravitation are, in all re- 
spects, equal. In many others the difference is only slight, yet in all 
these higher systems there must exist a common centre of gravity. 

With the mind cleared, by these views, from all prejudice in favor of 
the necessary existence of some stupendous central globe, as far exceeding 
in magnitude the myriads of fixed stars by which it is surrounded as does 
the sun all the satellites of its system, we are prepared to inquire into the 
actual existence or non-existence of such a body. 

Admitting its invisibility, either in consequence of its distance or non- 
luminous character, there are yet remaining the means, not only of detect- 
ing its existence, but of discovering its position in space. In case such a 
body exists, the stars located nearest to it will be most completely sub- 
jected to its influence, and will show their proximity by the swiftness of 
their motion. Since it is possible to penetrate space in every direction, 
in case the stars of any particular region were endowed with a more rapid 
motion than all others, these would not fail to be discovered. But no 
such rapid motions have ever been detected, and hence it is now fair to 
conclude that such motions do not exist, and consequently no vast central 
globe can ever be found, because there is no evidence that such a body 
has any locality in space. 

The questions resolve itself, then, into a research for the common 
centre of gravity of all the stars composing our astral system, and the data 

12 



178 STRUCTURE OF THE UNIVERSE. 

for such an examination must be found in the direction of the solar 
motion, and in that of the proper motion of the fixed stars. Difficult as 
this research undoubtedly is, Maedler's sagacity detected various guides 
which limited his more minute examinations to a comparatively small 
portion of the heavens. Since our great astral system has been shown to 
take the form of a layer or stratum whose thickness is small compared 
with its extent, we cannot fail to perceive that the centre of gravity of a 
mass of stars thus arranged must be found somewhere within the limits 
of the Milky Way, when seen by an eye located not very distant from the 
centre. But it is seen that our sun does not occupy the absolute centre 
of this stratum. In case it did, then would the bright circle of the Milky 
Way divide the heavens into two equal hemispheres. Since there is a 
manifest difference between the two parts into which the heavens is divid- 
ed, the smaller portion will be the more distant from us, and in this 
smaller part we must look for the central point. But, from the soundings 
of both the Herschels, it is certain that our sun lies nearer the southern 
half of the Milky Way than the northern. Hence, in our researches for 
the centre of gravity, we may confine our examinations to the northern 
half of the smaller of the two parts into which the Milky Way divides 
the heavens. 

One more approximation may be made. If we knew that our sun, in 
its presumed revolution about this great centre, described a circle, and if 
we knew the plane of this circle, and the direction in which the sun was 
now moving, a line drawn in that plane from the sun, and in a direction 
perpendicular to its line of motion, would pass directly through the centre 
about which it is revolving, and would point us directly to it. Now the 
direction of the sun's motion is alone determined ; but since the centre 
of gravity must be found somewhere in a line perpendicular to the direc- 
tion, we must give to this perpendicular all possible positions in space, 
which will cause it to cut from the celestial sphere the circumference of a 
great circle, within which the centre of gravity must be found. — These 
limiting considerations brought the distinguished astronomer to a region 
of the heavens in and about the constellation Taurus. 

Here the examination took a more definite and more strictly scientific 
form. The proper motion of the stars in this region could be anticipated 
and known, at least in character and direction. The great centre would 
probably be located within the limits of some rich cluster. All the stars 
composing this cluster as well as those within 20° or 30°, would appear to 
move in the same direction. Those immediately proximate to the central 
sun or star would appear to move with the same velocity due to that star, 
and the entire group would sweep, apparently, through space without 
parting compan}'. 

Having, by such like considerations, narrowed down the limits of 
research, Maedler commenced his individual examinations. Among other 



THE MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 179 

objects subjected to rigid scrutiny, was the brilliant star Aldebaran, in the 
eye of the Bull. This being the brightest star in this region, and being, 
moreover, in the midst of a group of smaller stars, seemed, in the outset, 
to fulfill some of the conditions required of the central sun. But a more 
rigid examination proved conclusively that this star could not occupy the 
centre. Its own proper motion far exceeded that of the surrounding 
stars, and demonstrated its near proximity to our own system, and its 
mere optical connection with the stars surrounding it. 

Thus did this great astronomer move from point to point, from star to 
star, subjecting eaeh successively to the severest tests, until, finally, a 
point was found, a star was discovered, fulfilling, in the most remarkable 
manner, all the requisitions demanded by the nature of the problem. All 
are familiar with the beautiful little cluster, called the Pleiades, or seven 
stars. Clustered around the brilliant star Alcyone, which occupies the 
optical^ centre of the group, the telescope shows fourteen conspicuous 
stars. The proper motions of all these have been determined with great 
exactitude. These are all in the same direction, and are all nearly equal 
to each other ; and, what is still more important, the mean of their proper 
motions differs from that of the central star, Alcyone, by only one thou- 
sandth of a second of arc in right ascension, and by two-thousanth's of a 
second in inclination. — Here, then, is a magnificent group of suns, either 
actually allied together, and sweeping in company through space, or else 
they compose a cluster so situated as to be affected by the same apparent 
motion produced by the sun's progressive motion through the celestial 
regions. 

But an extension of the limits of research around Alcyone exhibits the 
wonderful truth, that out of one hundred and ten stars within 15° of this 
centre, there are sixty moving south, or in accordance with the hypothesis 
that Alcyone is the centre, forty-nine exhibiting no well defined motion, 
and only one single individual which appears to move contrary to the 
computed direction ! 

It is impossible, here, to do justice to the profound and elaborate in- 
vestigations of the learned author of this great speculation. Assuming 
Alc}^one as the grand centre of the millions of stars composing our astral 
system, and the direction of the sun's motion, as determined by Argelander 
and Struve, he investigates the consequent movements of all the stars in 
every quarter of the heavens. Just where the swiftest motions should be 
found, there they actually exist, either demonstrating the truth of the 
theory, or exhibiting the most remarkable and incredible coincidences. 
We shall not pursue the research. After a profound examination, 
Maedler reaches the conclusion that Alcyone, the principal star in the 
group of the Pleiades, noiv occupies the centre of gravity, and is at present 
the su7i about which the universe of stars composing our astral system are all 
revolving. 



180 STRUCTURE OF THE UNIVERSE. 

Here, then, we stand on the confines of the unknown. One mighty 
effort has thus been made to bring beauty and order out of the chaos if 
motion which has hitherto distinguished the stars of heaven. Once the 
planets, freed from law, darted through space, or relaxing their speed ac- 
tually turned back on their unknown routes. Chaos reigned among 
these flying globes until the mind, rising by the efforts of its own genius, 
reached the grand centre of the planetary orbs, and lo ! confusion ceased, 
and harmony and beauty held their sway among these circling worlds. 
The same daring human genius which, sweeping across the interplanetary 
spaces, finally reached the controlling centre of our own great system, 
has now boldly plunged into the depths of space, has swept across the in> 
terstellar spaces, and roaming from star to star, from sun to sun, from 
system to system, looks out upon the universe of stars,' and seeks that 
point from whence these millions of sweeping suns shall exhibit that- 
grand and magnificent harmony which doubtless reigns throughout the 
vast empire of Jehovah. 

We are too apt to turn away from the first efforts to resolve these 
mighty problems. How were the doctrines of Newton received? How 
much regard was paid to Herschel's grand theory of the solar motion ? 
And yet how triumphantly have these great theories been established. 
But do you inquire if there be any possibility of proving or disproving 
the doctrines of Maedler ? The answer is simple. Should the time ever 
come when the direction of the solar motion shall be sensibly changed, in 
consequence of its curvilinear character, then will the plane in which this 
movement lies be revealed, and then the centre about which the revolu- 
tion is performed must be made known, at least in direction. Should the 
line reaching towards this grand centre pass through Alcyone this added 
to all the other evidences, will fix forever the question of its central posi- 
tion. We know not when this great question may be settled, but judg- 
ing from the triumphs which have marked the career of human genius 
hitherto, we do not dare to doubt of the final result. 

Admitting the truth of Maedler's theory, we are led to some of the 
most astonishing results. The known parallax of certain fixed stars gives 
to us an approximate value of the parallax of Alcyone, and reveals to us the 
distance of the grand centre. Such is the enormous interval separating 
the sun from the central star about which it performs its mighty revolu- 
tion, that the light from Alcyone requires a period of 537 years to trav- 
erse the distance ! And if we are to rely on the angular motion of the sun 
and system, as already determined, «tt the end of 18,200,000 years, this 
great luminary, with all its planets, satellites, and comets, will have com- 
pleted one revolution around its grand centre ! 

Look out to-night on the brilliant constellations which crowd the heav- 
ens. Mark the configurations of these stars. Five thousand years ago 
the Chaldean shepherd gazed on the same bright groups. — Two thousand 



THE MOTIONS AND REVOLUTIONS OF THE FIXED STABS. 181 

years have rolled away since the Greek philosopher pronounced the 
eternity of the heavens, and pointed to the ever-during configuration of 
the stars as proof positive of his assertion. But a time will come when 
not a constellation now blazing in the bright concave above us shall re- 
main. Slowly, indeed, do these fingers on the dial of heaven mark the 
progress of time. A thousand years may roll away with scarce a per- 
ceptible change ; — even a million of years may pass without effacing all 
traces of the groupings which now exist ; but that eye which shall behold 
the universe of the fixed stars when ten millions of years shall have 
silently rolled away, will search in vain for the constellations which now 
beautify and adorn our nocturnal heavens. Should God permit, the stars 
may be there, but no trace of their former relative positions will be 
found ! 

Here I must close. The intellectual power of man, as exhibited in his 
wonderful achievements among the planetary and stellar worlds, has thus 
far been our single object. I have neither turned to the right hand nor 
to the left. Commencing with the first mute gaze bestowed upon the 
heavens, and with the curiosity awakened in that hour of admiration and 
wonder, we have attempted to follow rapidly the career of the human 
mind, through the long lapse of six thousand years. What a change has 
this period wrought. Go backward in imagination to the plains of 
Shinar, and stand beside the shepherd astronomer as he vainly attempts 
to grasp the mysteries of the waxing and waning moon, and then enter 
the sacred precincts of yonder temple devoted to the science of the stars. 
— Look over its magnificent machinery ; examine its space-annihilating 
instruments, and ask the sentinel who now keeps his unbroken vigil, the 
nature of his investigations. 

Moon, and planet, and sun, and system, are left behind. His researches 
are now within a sphere to whose confines the eagle glance of the Chal- 
dean never reached. Periods, and distances, and masses, and motions, 
are all familiar to him, «and could the man who gazed and pondered six 
thousand years ago stand beside the man who now fills his place, and lis- 
ten to his teachings, he would listen with awe, inspired by the revelations 
of an angel of God. But where does the human mind now stand ? Great 
as are its achievements, profoundly as it has penetrated the mysteries of 
creation, what has been done is but an infinitesimal portion of what 
remains to be done. 

But the examinations of the past inspire the highest hopes for the fu- 
ture. The movement is one constantly accelerating and expanding. Look 
at what has been done during the last three hundred years, and answer 
me to what point will human genius ascend, before the same period shall 
again roll away ? But in our admiration for that genius which has been 
able to reveal the mysteries of the universe, let us not forget the homage 
due to Him who created, and by the might of his power sustains all things. 



Ig2 STRUCTURE OF THE UNIVERSE. 

At some future time, I hope to be permitted to direct your attention to 
this branch of the subject. If there be anything which can lead the mind 
upward to the Omnipotent Ruler of the universe, and give to it an approx- 
imate knowledge of His incomprehensible attributes, it is to be found in 
the grandeur and beauty of His works. 

If you would know his glory, examine the interminable range of suns 
and systems which crowd the Milky Way. — Multiply the hundred millions 
of stars which belong to our own " island universe " by the thousands of 
these astral systems that exist in space, within the range of human vision, 
and then you may form some idea of the infinitude of his kingdom ; for 
]o ! these are but a part of his ways. Examine the scale on which the uni- 
verse is built. — Comprehend, if you can, the vast dimensions of our sun. 
— Stretch outward through his system, from planet to planet, and cir- 
cumscribe the whole within the immense circumference of Neptune's orbit. 
This is but a single unit out of the myriads of similar systems. Take the 
wings of light, and flash with impetuous speed day and night, and month, 
and year, till youth shall wear away, and middle age is gone, and the ex- 
tremest limit of human life has been attained ; — count every pulse, and at 
each speed on your way a hundred thousand miles; and when a hundred 
years have rolled by, look out, and behold ! the thronging millions of blaz- 
ing suns are still around you, each separated from the other by such a dis- 
tance that in this journey of a century you have only left half a score be- 
hind you. 

Would you gather some idea of the eternity past of God's existence, go 
to the astronomer, and bid him lead you with him in one of his walks 
through space ; and as he sweeps outward from object to object, from uni- 
verse to universe, remember that the light from those filmy stains on the 
deep pure blue heaven, now falling on your eye, has been traversing space 
for a million of years. Would you gather some knowledge of the omnipotence 
of God, weigh the earth on which we dwell, then count the millions of its 
inhabitants that have come and gone for the last six thousand years. Unite 
their strength into one arm, and test its power in an effort to move this 
earth. It could not stir it a single foot in a thousand years ; and yet un- 
der the omnipotent hand of God, not a minute passes that it does not fly 
for more than a thousand miles. But this is a mere atom ; — the most insig- 
nificant point among his innumerable worlds. At his bidding, every plan- 
et, and satellite and comet, and the sun himself, fly onward in their ap- 
pointed courses. His single arm guides the millions of sweeping suns, and 
around His throne circles the great constellation of unnumbered universes. 

Would you comprehend the idea of the omniscience of God, remember 
that the highest pinnacle of knowledge reached by the whole human race, 
by the combined efforts of its brightest intellects, has enabled the astrono- 
mer to compute approximately the perturbations of the planetary worlds. 
He has predicted roughly the return of half a score of comets. But God 



THE MOTIONS AND REVOLUTIONS OF THE FIXED STABS. 183 

has computed the mutual perturbations of millions of suns, and planets, 
and comets, and worlds, without number, through the ages that are passed 
and throughout the ages which are yet to come, not approximately, but 
with perfect and absolute precision. The universe is in motion, — system 
rising above system cluster above cluster, nebula above nebula, — all majes- 
tically sweeping around under the providence of God, who alone knows 
the end from the beginning, and before whose glory and power all intelli- 
gent beings, whether in heaven or on earth, should bow with humility 
and awe. 

Would you gain some idea of the wisdom of God, look to the admira- 
ble adjustments of the magnificent retinue of planets and satellites which 
sweep around the sun. Every globe has been weighed and poised, every 
orbit has been measured and bent to its beautiful form. All is chang- 
ing, but the laws fixed by the wisdom of God, though they permit the 
rocking to and fro of the system, never introduce disorder, or lead to de- 
struction. All is perfect and harmonious, and the music of the spheres 
that burn and roll around our sun, is echoed by that of ten millions of 
moving worlds, that sing and shine around the bright suns that reign 
above. * 

If overwhelmed with the grandeur and majesty of the universe of God, 
we are led to exclaim with the Hebrew poet king, — " When I consider 
thy heavens, the work of thy fingers, the moon and the stars which thou 
hast ordained, what is man that thou art mindful of him ? and the son of 
man, that thou visitests him ? " If fearful that the eye of God may over- 
look us in the immensity of his kingdom, we have only to call to mind that 
other passage, "Yet thou hast made him but a little lower than the an- 
gels, and hast crowned him with glory and honor. Thou madest him to 
have dominion over all the works of thy hand ; thou hast put all 
things under his feet." Such are the teachings of the word, and such 
are the lessons of the works of God. 



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